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Keywords = synchronous oscillation

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18 pages, 3585 KB  
Article
Frontal Theta Oscillations in Perceptual Decision-Making Reflect Cognitive Control and Confidence
by Rashmi Parajuli, Eleanor Flynn and Mukesh Dhamala
Brain Sci. 2026, 16(2), 123; https://doi.org/10.3390/brainsci16020123 - 23 Jan 2026
Viewed by 74
Abstract
Background: Perceptual decision-making requires transforming sensory inputs into goal-directed actions under uncertainty. Neural oscillations in the theta band (3–7 Hz), particularly within frontal regions, have been implicated in cognitive control and decision confidence. However, whether changes in theta oscillations reflect greater effort during [...] Read more.
Background: Perceptual decision-making requires transforming sensory inputs into goal-directed actions under uncertainty. Neural oscillations in the theta band (3–7 Hz), particularly within frontal regions, have been implicated in cognitive control and decision confidence. However, whether changes in theta oscillations reflect greater effort during ambiguous decisions or more efficient control during clear conditions remains debated, and theta’s relationship to stimulus clarity is incompletely understood. Purpose: This study’s purpose was to examine how task difficulty modulates theta activity and how theta dynamics evolve across the decision-making process using two complementary analytical approaches. Methods: Electroencephalography (EEG) data were acquired from 26 healthy adults performing a face/house categorization task with images containing three levels of scrambled phase and Gaussian noise: clear (0%), moderate (40%), and high (55%). Theta dynamics were assessed from current source density (CSD) time courses of event-related potentials (ERPs) and single-trials. Statistical comparisons used Wilcoxon signed-rank tests with false discovery rate (FDR) correction for multiple comparisons. Results: Frontal theta power was greater for clear than noisy face stimuli (corrected p < 0.001), suggesting that theta activity reflects cognitive control effectiveness and decision confidence rather than processing difficulty. Connectivity decomposition revealed that frontoparietal theta coupling was modulated by stimulus clarity through both phase-locked (evoked: corrected p = 0.0085, dz = −0.61) and ongoing (induced: corrected p = 0.049, dz = −0.36) synchronization, with phase-locked coordination dominating the effect and showing opposite directionality to the induced components. Conclusions: Theta oscillations support perceptual decision-making through stimulus clarity modulation of both phase-locked and ongoing synchronization, with evoked component dominating. These findings underscore the importance of methodological choices in EEG-based connectivity research, as different analytical approaches capture different aspects of the same neural dynamics. The pattern of stronger theta activity for clear stimuli is consistent with neural processes related to decision confidence, though confidence was not measured behaviorally. Full article
(This article belongs to the Section Cognitive, Social and Affective Neuroscience)
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19 pages, 1516 KB  
Article
Energy-Dynamics Sensing for Health-Responsive Virtual Synchronous Generator in Battery Energy Storage Systems
by Yingying Chen, Xinghu Liu and Yongfeng Fu
Batteries 2026, 12(1), 36; https://doi.org/10.3390/batteries12010036 - 21 Jan 2026
Viewed by 76
Abstract
Battery energy storage systems (BESSs) are increasingly required to provide grid-support services under weak-grid conditions, where the stability of virtual synchronous generator (VSG) control largely depends on the health status and dynamic characteristics of the battery unit. However, existing VSG strategies typically assume [...] Read more.
Battery energy storage systems (BESSs) are increasingly required to provide grid-support services under weak-grid conditions, where the stability of virtual synchronous generator (VSG) control largely depends on the health status and dynamic characteristics of the battery unit. However, existing VSG strategies typically assume fixed parameters and neglect the intrinsic coupling between battery aging, DC-link energy variations, and converter dynamic performance, resulting in reduced damping, degraded transient regulation, and accelerated lifetime degradation. This paper proposes a health-responsive VSG control strategy enabled by real-time energy-dynamics sensing. By reconstructing the DC-link energy state from voltage and current measurements, an intrinsic indicator of battery health and instantaneous power capability is established. This energy-dynamics indicator is then embedded into the VSG inertia and damping loops, allowing the control parameters to adapt to battery health evolution and operating conditions. The proposed method achieves coordinated enhancement of transient stability, weak-grid robustness, and lifetime management. Simulation studies on a multi-unit BESS demonstrate that the proposed strategy effectively suppresses low-frequency oscillations, accelerates transient convergence, and maintains stability across different aging stages. Full article
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21 pages, 3790 KB  
Article
HiLTS©: Human-in-the-Loop Therapeutic System: A Wireless-Enabled Digital Neuromodulation Testbed for Brainwave Entrainment
by Arfan Ghani
Technologies 2026, 14(1), 71; https://doi.org/10.3390/technologies14010071 - 18 Jan 2026
Viewed by 179
Abstract
Epileptic seizures arise from abnormally synchronized neural activity and remain a major global health challenge, affecting more than 50 million people worldwide. Despite advances in pharmacological interventions, a significant proportion of patients continue to experience uncontrolled seizures, underscoring the need for alternative neuromodulation [...] Read more.
Epileptic seizures arise from abnormally synchronized neural activity and remain a major global health challenge, affecting more than 50 million people worldwide. Despite advances in pharmacological interventions, a significant proportion of patients continue to experience uncontrolled seizures, underscoring the need for alternative neuromodulation strategies. Rhythmic neural entrainment has recently emerged as a promising mechanism for disrupting pathological synchrony, but most existing systems rely on complex analog electronics or high-power stimulation hardware. This study investigates a proof-of-concept digital custom-designed chip that generates a stable 6 Hz oscillation capable of imposing a stable rhythmic pattern onto digitized seizure-like EEG dynamics. Using a publicly available EEG seizure dataset, we extracted and averaged analog seizure waveforms, digitized them to emulate neural front-ends, and directly interfaced the digitized signals with digital output recordings acquired from the chip using a Saleae Logic analyser. The chip’s pulse train was resampled and low-pass-reconstructed to produce an analog 6 Hz waveform, allowing direct comparison between seizure morphology, its digitized representation, and the entrained output. Frequency-domain and time-domain analyses demonstrate that the chip imposes a narrow-band 6 Hz rhythm that overrides the broadband spectral profile of seizure activity. These results provide a proof-of-concept for low-power digital custom-designed entrainment as a potential pathway toward simplified, wearable neuromodulation device for future healthcare diagnostics. Full article
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13 pages, 3377 KB  
Article
Clock Synchronization with Kuramoto Oscillators for Space Systems
by Nathaniel Ristoff, Hunter Kettering and James Camparo
Time Space 2026, 2(1), 1; https://doi.org/10.3390/timespace2010001 - 15 Jan 2026
Viewed by 101
Abstract
As space systems evolve towards cis-lunar missions and beyond, the demand for precise yet low-size, -weight, and -power (SWaP) clocks and synchronization methods becomes increasingly critical. We introduce a novel clock synchronization approach based on the Kuramoto oscillator model that facilitates the creation [...] Read more.
As space systems evolve towards cis-lunar missions and beyond, the demand for precise yet low-size, -weight, and -power (SWaP) clocks and synchronization methods becomes increasingly critical. We introduce a novel clock synchronization approach based on the Kuramoto oscillator model that facilitates the creation of an ensemble timescale for satellite constellations. Unlike traditional ensembling algorithms, the proposed Kuramoto method leverages nearest-neighbor interactions to achieve collective synchronization. This method simplifies the communication architecture and data-sharing requirements, making it well suited for dynamically connected networks such as proliferated low Earth orbit (pLEO) and lunar or Martian constellations, where intersatellite links may frequently change. Through simulations incorporating realistic noise models for small-scale atomic clocks, we demonstrate that the Kuramoto ensemble can yield an improvement in stability on the order of 1/√N, while mitigating the impact of constellation fragmentation and defragmentation. The results indicate that the Kuramoto oscillator-based algorithm can potentially deliver performance comparable to established techniques like Equal Weights Frequency Averaging (EWFA), yet with enhanced scalability and resource efficiency critical for future spaceborne PNT and communication systems. Full article
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22 pages, 7325 KB  
Review
Adaptive Virtual Synchronous Generator Control Using a Backpropagation Neural Network with Enhanced Stability
by Hanzhong Chen, Huangqing Xiao, Kai Gong, Zhengjian Chen and Wenqiao Qiang
Electronics 2026, 15(2), 333; https://doi.org/10.3390/electronics15020333 - 12 Jan 2026
Viewed by 110
Abstract
To enhance grid stability with high renewable energy penetration, this paper proposes an adaptive virtual synchronous generator (VSG) control using a backpropagation neural network (BPNN). Traditional VSG control methods exhibit limitations in handling nonlinear dynamics and suppressing power oscillations. Distinguishing from existing studies [...] Read more.
To enhance grid stability with high renewable energy penetration, this paper proposes an adaptive virtual synchronous generator (VSG) control using a backpropagation neural network (BPNN). Traditional VSG control methods exhibit limitations in handling nonlinear dynamics and suppressing power oscillations. Distinguishing from existing studies that apply BPNN solely for damping adjustment, this paper proposes a novel strategy where BPNN simultaneously regulates both VSG virtual inertia and damping coefficients by learning nonlinear relationships among inertia, angular velocity deviation, and its rate of change. A key innovation is redesigning the error function to minimize angular acceleration changes rather than frequency deviations, aligning with rotational inertia’s physical role and preventing excessive adjustments. Additionally, an adaptive damping coefficient is introduced based on optimal damping ratio principles to further suppress power oscillations. Simulation under load disturbances and grid frequency perturbations demonstrates that the proposed BPNN strategy significantly outperforms constant inertia, bang–bang, and radial basis function neural network methods. Full article
(This article belongs to the Section Industrial Electronics)
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18 pages, 2837 KB  
Article
Grid-Connected Active Support and Oscillation Suppression Strategy of Energy Storage System Based on Virtual Synchronous Generator
by Zhuan Zhao, Jinming Yao, Shuhuai Shi, Di Wang, Duo Xu and Jingxian Zhang
Electronics 2026, 15(2), 323; https://doi.org/10.3390/electronics15020323 - 11 Jan 2026
Viewed by 131
Abstract
This paper addresses stability issues, including voltage fluctuation, a frequency offset, and broadband oscillation resulting from the high penetration of renewable energy in a photovoltaic high-permeability distribution network. This paper proposes an active support control strategy which is energy storage grid-connected based on [...] Read more.
This paper addresses stability issues, including voltage fluctuation, a frequency offset, and broadband oscillation resulting from the high penetration of renewable energy in a photovoltaic high-permeability distribution network. This paper proposes an active support control strategy which is energy storage grid-connected based on a virtual synchronous generator (VSG). This strategy endows the energy storage system with virtual inertia and a damping capacity by simulating the rotor motion equation and excitation regulation characteristics of the synchronous generator, and effectively enhances the system’s ability to suppress power disturbances. The small-signal model of the VSG system is established, and the influence mechanism of the virtual inertia and damping coefficient on the system stability is revealed. A delay compensator in series with a current feedback path is proposed. Combined with the damping optimization of the LCL filter, the instability risk caused by high-frequency resonance and a control delay is significantly suppressed. The novelty lies in the specific configuration of the compensator within the grid–current feedback loop and its coordinated design with VSG parameters, which differs from traditional capacitive–current feedback compensation methods. The experimental results obtained from a semi-physical simulation platform demonstrate that the proposed control strategy can effectively suppress voltage fluctuations, suppress broadband oscillations, and improve the dynamic response performance and fault ride-through capability of the system under typical disturbance scenarios such as sudden illumination changes, load switching, and grid faults. It provides a feasible technical path for the stable operation of the distribution network with a high proportion of new energy access. Full article
(This article belongs to the Special Issue Innovations in Intelligent Microgrid Operation and Control)
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19 pages, 16366 KB  
Article
A Supplementary Damping Control of D-STATCOM for Alleviating SSO in Photovoltaic Generation Integrated into Weak AC Grid
by Qichao Chen, Nan Wei, Zhidong Wang, Zhi An, Peng Tao and Yiqi Liu
Energies 2026, 19(1), 234; https://doi.org/10.3390/en19010234 - 31 Dec 2025
Viewed by 255
Abstract
The interaction between the Photovoltaic station and the weak grid can easily trigger sub- or super-synchronous oscillation (SSO). In this article, the equivalent impedance model of the photovoltaic grid-connected system is built, and the mechanism of SSO is analyzed based on the global [...] Read more.
The interaction between the Photovoltaic station and the weak grid can easily trigger sub- or super-synchronous oscillation (SSO). In this article, the equivalent impedance model of the photovoltaic grid-connected system is built, and the mechanism of SSO is analyzed based on the global admittance criterion (GA). To mitigate the SSO, a Distribution Static Synchronous Compensator (D-STATCOM) supplementary damping control (SDC) strategy is proposed, which uses a three-parameter notch filter to extract the sub- or super-synchronous harmonic component without a phase shift. The component is superimposed on the modulated wave of the D-STATCOM through the gain link to obtain the modulation instruction. At the sub- or super-synchronous frequency, the D-STATCOM can be equivalent to the parallel impedance in the system and play a role in suppressing the sub- or super-synchronous oscillation. Compared to the complex combination filters in the traditional SDC, which require phase compensation and have poor adaptability, the three-parameter notch filter used in this SDC does not need a phase compensation stage and can effectively cope with the presence of oscillation frequencies on both sides of the fundamental frequency with a simpler design. Simulation results prove that the proposed scheme effectively improves the stability of photovoltaic generation under different short-circuit ratios, irradiance levels, and fault conditions. The proposed solution can be applied to photovoltaic generation equipped with D-STATCOM. Full article
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36 pages, 6311 KB  
Article
Implementation of a QDBC with Hysteresis Current Control for PV-Powered Permanent-Magnet-Assisted Synchronous Reluctance Motors
by Walid Emar, Hani Attar, Ala Jaber, Hasan Kanaker, Fawzi Gharagheer and Musbah Aqel
Energies 2026, 19(1), 215; https://doi.org/10.3390/en19010215 - 31 Dec 2025
Viewed by 159
Abstract
In this paper, a permanent-magnet-assisted synchronous reluctance motor (SYNRM) coupled with a newly built QDBC and a voltage-fed inverter (VFI) for a standalone PV water pumping system is suggested. Because power supply oscillations can result in short-term disruptions that affect drive performance in [...] Read more.
In this paper, a permanent-magnet-assisted synchronous reluctance motor (SYNRM) coupled with a newly built QDBC and a voltage-fed inverter (VFI) for a standalone PV water pumping system is suggested. Because power supply oscillations can result in short-term disruptions that affect drive performance in industrial applications involving these motors, a robust smooth control system is required to guarantee high efficiency and uninterrupted operation. According to the suggested architecture, a newly built quadratic boost regulator with a very high voltage gain, called a quadruple-diode boost converter (QDBC), is used to first elevate PV voltage to high levels. Additionally, to optimize the power output of the solar PV module, the perturbation and observation highest power point tracking approach (P&O) is implemented. To provide smooth synchronous motor starting, field-oriented control (FOC) of a voltage-fed inverter (VFI) is combined with hysteresis current control of the QDBC. The optimization algorithms discussed in this paper aim to enhance the efficiency of the SYNRM, particularly in operating a synchronous motor powered by variable energy sources such as solar PV. These algorithms function within a cybernetic system designed for water pumping, incorporating feedback loops and computational intelligence for improved performance. Afterward, the three-phase permanent-magnet synchronous motor that drives the mechanical load is fed by the resulting voltage via a voltage source inverter. Furthermore, a thorough hysteresis current control method implementation of the QDBC was suggested in order to attain optimal efficiency in both devices, which is crucial when off-grids are present. Even when the DC-link voltage dropped by up to 10% of the rated voltage, the suggested method was shown to maintain the required reference torque and rated speed. To verify the efficacy of the suggested method, a simulation setup according to the MATLAB 2022b/Simulink environment was employed. To gather and analyze the data, multiple scenarios with varying operating conditions and irradiance levels were taken into consideration. Finally, a working prototype was constructed in order to validate the mathematical analysis and simulation findings of the suggested framework, which includes a 1 kW motor, current sensor, voltage sensor, QDBC, and VCS inverter. Full article
(This article belongs to the Section F3: Power Electronics)
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18 pages, 7746 KB  
Article
A Multicomponent OBN Time-Shift Joint Correction Method Based on P-Wave Empirical Green’s Functions
by Dongxiao Jiang, Bingyu Chen, Lei Cheng, Chang Chen, Yingda Li and Yun Wang
J. Mar. Sci. Eng. 2026, 14(1), 60; https://doi.org/10.3390/jmse14010060 - 29 Dec 2025
Viewed by 296
Abstract
To address clock drift arising from the absence of GPS synchronization during ocean-bottom seismic observations, we propose a time-offset correction and quality-control scheme that uses the correlation of P-wave empirical Green’s functions (EGFs) as the metric, and we demonstrate its efficacy in mitigating [...] Read more.
To address clock drift arising from the absence of GPS synchronization during ocean-bottom seismic observations, we propose a time-offset correction and quality-control scheme that uses the correlation of P-wave empirical Green’s functions (EGFs) as the metric, and we demonstrate its efficacy in mitigating cross-correlation asymmetry caused by azimuthal noise in shallow-water environments. The method unifies the time delays of the four components into a single objective function, estimates per-node offsets via sparse weighted least squares with component-specific weights, applies spatial second-difference smoothing to suppress high-frequency oscillations, and performs spatiotemporally constrained regularized iterative optimization initialized by the previous day’s inversion to achieve a robust solution. Tests on a real four-component ocean-bottom node (4C-OBN) hydrocarbon exploration dataset show that, after conventional linear clock-drift correction of the OBN system, the proposed method can effectively detect millisecond-scale time jumps on individual nodes; compared with traditional noise cross-correlation time-shift calibration based on surface-wave symmetry, our four-component fusion approach achieves superior robustness and accuracy. The results demonstrate a marked increase in the coherence of the four-component cross-correlations after correction, providing a reliable temporal reference for subsequent multicomponent seismic processing and quality control. Full article
(This article belongs to the Section Geological Oceanography)
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22 pages, 2470 KB  
Article
Dynamic Synchronization and Resonance as the Origin of 1/f Fluctuations—Amplitude Modulation Across Music and Nature
by Akika Nakamichi, Izumi Uesaka and Masahiro Morikawa
Entropy 2026, 28(1), 38; https://doi.org/10.3390/e28010038 - 27 Dec 2025
Viewed by 314
Abstract
In natural systems, astrophysics, biological physics, and social physics, 1/f fluctuations are observed across a wide range of systems. Focusing on the case of music, we propose and verify a physical mechanism for generating these fluctuations. This mechanism is based on amplitude modulation [...] Read more.
In natural systems, astrophysics, biological physics, and social physics, 1/f fluctuations are observed across a wide range of systems. Focusing on the case of music, we propose and verify a physical mechanism for generating these fluctuations. This mechanism is based on amplitude modulation (AM) and demodulation (DM), where the 1/f spectral law appears not in the raw waveform but in its demodulated amplitude envelope. Two distinct yet complementary processes generate the required AM: (i) stochastic synchronization among oscillators, modeled via an extended Kuramoto framework that captures perpetual synchronization–desynchronization cycles, and (ii) frequency-selective resonance, modeled by spectral accumulation of eigenmodes in acoustic or structural environments. Numerical simulations demonstrate that both mechanisms, acting alone or in combination, robustly generate 1/f spectra spanning several digits when demodulation is applied and that the classical Kuramoto critical point is not essential for its emergence. While this analysis focuses on 1/f fluctuations in musical performance and acoustics, we also note that 1/f fluctuations inherent in musical scores may be similarly described by the AM/DM mechanism. Full article
(This article belongs to the Section Statistical Physics)
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12 pages, 610 KB  
Article
Estimation of Information Flow-Based Causality with Coarsely Sampled Time Series
by X. San Liang
Entropy 2026, 28(1), 34; https://doi.org/10.3390/e28010034 - 26 Dec 2025
Viewed by 344
Abstract
The past decade has seen growing applications of the information flow-based causality analysis, particularly with the concise formula of its maximum likelihood estimator. At present, the algorithm for its estimation is based on differential dynamical systems, which, however, may raise an issue for [...] Read more.
The past decade has seen growing applications of the information flow-based causality analysis, particularly with the concise formula of its maximum likelihood estimator. At present, the algorithm for its estimation is based on differential dynamical systems, which, however, may raise an issue for coarsely sampled time series. Here, we show that, for linear systems, this is suitable at least qualitatively, but, for highly nonlinear systems, the bias increases significantly as the sampling frequency is reduced. This study provides a partial solution to this problem, showing how causality analysis can be made faithful with coarsely sampled series, provided that the statistics are sufficient. The key point here is that, instead of working with a Lie algebra, we turn to work with its corresponding Lie group. An explicit and concise formula is obtained, with only sample covariances involved. It is successfully applied to a system comprising a pair of coupled Rössler oscillators. Particularly remarkable is the success when the two oscillators are nearly synchronized. As more often than not observations may be scarce, this solution, albeit partial, is very timely. Full article
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20 pages, 1586 KB  
Article
Evaluation of TRNG Bit Distribution via Stable Entropy Source Synchronization on FPGA
by Ryoichi Sato, Mitsuki Fujiwara, Yasuyuki Nogami, Md Arshad Ali and Yuta Kodera
Entropy 2026, 28(1), 31; https://doi.org/10.3390/e28010031 - 26 Dec 2025
Viewed by 267
Abstract
This study examined the correlation between the number of delay flip-flops (D-FFs) connected after each ring oscillator (RO) and the bit distribution of random number sequences in an RO-based random number generator (RNG). In our previous research, unstable input signals to the XOR [...] Read more.
This study examined the correlation between the number of delay flip-flops (D-FFs) connected after each ring oscillator (RO) and the bit distribution of random number sequences in an RO-based random number generator (RNG). In our previous research, unstable input signals to the XOR gate contributed to differences in bit distribution. Based on these results, we simulated how combining signals with biased distributions through XOR gates affects the overall bit distribution. Beyond this, we also conducted simulations where the inputs to the XOR gate included not just {0, 1} signals, but also three-state signals incorporating metastable states. We then proposed using multi-D-FFs as synchronization circuits for RO signals and performed analyses on RO-based RNG implementations by estimating metastable output conditions and conducting NIST Special Publication 800-22 tests regarding bit distributions. These results confirm that inserting two or more D-FFs after RO signals improves the bit distribution of RO-based RNG implementations. Full article
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26 pages, 1023 KB  
Article
Secure Signal Encryption in IoT and 5G/6G Networks via Bio-Inspired Optimization of Sprott Chaotic Oscillator Synchronization
by Fouzia Maamri, Hanane Djellab, Sofiane Bououden, Farouk Boumehrez, Abdelhakim Sahour, Mohamad A. Alawad, Ilyes Boulkaibet and Yazeed Alkhrijah
Entropy 2026, 28(1), 30; https://doi.org/10.3390/e28010030 - 26 Dec 2025
Viewed by 318
Abstract
The rapid growth of Internet of Things (IoT) devices and the emergence of 5G/6G networks have created major challenges in secure and reliable data transmission. Traditional cryptographic algorithms, while robust, often suffer from high computational complexity and latency, making them less suitable for [...] Read more.
The rapid growth of Internet of Things (IoT) devices and the emergence of 5G/6G networks have created major challenges in secure and reliable data transmission. Traditional cryptographic algorithms, while robust, often suffer from high computational complexity and latency, making them less suitable for large-scale, real-time applications. This paper proposes a chaos-based encryption framework that uses the Sprott chaotic oscillator to generate secure and unpredictable signals for encryption. To achieve accurate synchronization between the transmitter and the receiver, two bio-inspired metaheuristic algorithms—the Pachycondyla Apicalis Algorithm (API) and the Penguin Search Optimization Algorithm (PeSOA)—are employed to identify the optimal control parameters of the Sprott system. This optimization improves synchronization accuracy and reduces computational overhead. Simulation results show that PeSOA-based synchronization outperforms API in convergence speed and Root Mean Square Error (RMSE). The proposed framework provides robust, scalable, and low-latency encryption for IoT and 5G/6G networks, where massive connectivity and real-time data protection are essential. Full article
(This article belongs to the Section Complexity)
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25 pages, 1828 KB  
Article
A Novel Butterfly-Attractor Dynamical System Without Equilibrium: Theory, Synchronization, and Application in Secure Communication
by Viet-Thanh Pham, Victor Kamdoum Tamba, Fernando E. Serrano, Giuseppe Grassi and Shaher Momani
Algorithms 2026, 19(1), 18; https://doi.org/10.3390/a19010018 - 24 Dec 2025
Viewed by 479
Abstract
The theory underlying non-linear dynamical systems remains essential for understanding complex behaviors in science and engineering. In this study, we propose a new chaotic dynamical system that exhibits a butterfly-shaped attractor without any equilibrium point. Despite its compact structure comprising only five terms, [...] Read more.
The theory underlying non-linear dynamical systems remains essential for understanding complex behaviors in science and engineering. In this study, we propose a new chaotic dynamical system that exhibits a butterfly-shaped attractor without any equilibrium point. Despite its compact structure comprising only five terms, the system demonstrates rich chaotic behavior distinct from conventional oscillator models. Detailed modeling and dynamical analyses are conducted to confirm the presence of chaos and to characterize the system’s sensitivity to initial conditions. Furthermore, synchronization of the proposed dynamical system is investigated using both identical and non-identical control algorithms. In the identical case, the activation function of the neural network is governed by the butterfly oscillator dynamics, whereas in the non-identical case, a sigmoidal activation function is employed. The proposed synchronization algorithms enable faster convergence by pinning a subset of nodes in the network. Finally, a practical implementation of the conceived dynamical system in an encryption framework is presented, with the aim to demonstrate its feasibility and potential application in secure communication systems. The results highlight the effectiveness of the proposed approach for both theoretical exploration and engineering applications involving chaotic dynamical systems. Full article
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18 pages, 2592 KB  
Article
Transient Damping-Type VSG Control Strategy Based on Flexibly Adjustable Cutoff Frequency
by Zili Zhang, Jing Wu, Deshuai Wang, Junyuan Zhang, Mengwei Lou and Jianhui Meng
Electronics 2026, 15(1), 69; https://doi.org/10.3390/electronics15010069 - 23 Dec 2025
Viewed by 175
Abstract
To address the insufficient adaptability of virtual synchronous generators (VSGs) under traditional fixed-value damping control in multiple application scenarios and the lack of regulatory flexibility in transient damping control with a fixed cutoff frequency, a transient damping-type VSG control strategy with flexibly adjustable [...] Read more.
To address the insufficient adaptability of virtual synchronous generators (VSGs) under traditional fixed-value damping control in multiple application scenarios and the lack of regulatory flexibility in transient damping control with a fixed cutoff frequency, a transient damping-type VSG control strategy with flexibly adjustable cutoff frequency is proposed. The aim is to break through the regulatory limitations of the fixed cutoff frequency, quantify the inverse coordination relationship between the cutoff frequency and the equivalent damping coefficient, establish a dynamic adjustment mechanism of the cutoff frequency based on the system natural oscillation frequency, damping ratio, and power grid parameters, and clarify the value range from 0 to ωcmax as well as the real-time adaptation algorithm. First, the influence of damping on active power and frequency is analyzed through the VSG model. Second, combined with the characteristic analysis of different damping types, the advantages of transient damping in transient response capability under various operating conditions are derived. Furthermore, the role of the cutoff frequency in transient damping on output characteristics is specifically analyzed, a transient damping design method with flexibly adjustable cutoff frequency is proposed, and the value range of the cutoff frequency is calibrated. Finally, a hardware-in-the-loop experimental platform is established for experimental testing. The strategy effectively eliminates the output power deviation when the system frequency deviates, enhances the transient response capability of the VSG under different operating conditions, and exhibits superior output characteristics. Full article
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