Search Results (175)

This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness against disturbance in wireless environments. To be applied to embedded microprocessors, the continuous-time chaotic system is discretized using the Grunwald–Letnikov approximation. To avoid the loss of generality of chaotic behavior, Lyapunov exponents are computed to validate the preservation of chaos in the discrete-time domain. The FBELNN controller is then developed to synchronize two non-identical chaotic systems under different initial conditions, enabling secure data encryption and decryption. Additionally, the DOB is introduced to estimate and mitigate the effects of bounded uncertainties and external disturbances, enhancing the system’s resilience to stealthy attacks. The proposed control structure is experimentally implemented on a wireless communication system utilizing ESP32 microcontrollers (Espressif Systems, Shanghai, China) based on the ESP-NOW protocol. Both control and feedback signals of the electric drive system are encrypted using chaotic states, and real-time decryption at the receiver confirms system integrity. Experimental results verify the effectiveness of the proposed method in achieving robust synchronization, accurate signal recovery, and a reliable wireless control system. The combination of FBELNN and DOB demonstrates significant potential for real-time, low-cost, and secure applications in smart electric drive systems and industrial automation. Full article

In the era of digital communication, securing sensitive information against increasingly sophisticated cyber threats remains a critical challenge. Chaos synchronization, while promising for secure communication and control systems, faces key limitations, including high sensitivity to parameter mismatches and initial conditions, vulnerability to noise, and difficulties in maintaining stability for high-dimensional systems. This paper presents a novel secure communication system based on multi-level synchronization of three distinct chaotic systems: the Bhalekar–Gejji (BG) system, the Chen system, and a 3D chaotic oscillator. Utilizing the nonlinear active control (NAC) method, we achieve robust synchronization between master and slave systems, ensuring the stability of the error dynamics through Lyapunov theory. The proposed triple-cascade masking technique enhances security by sequentially embedding the information signal within the chaotic outputs of these systems, making decryption highly challenging without knowledge of all three systems. Numerical simulations and Simulink implementations validate the effectiveness of the synchronization and the secure communication scheme. The results demonstrate that the transmitted signal becomes unpredictable and resistant to attacks, significantly improving the security of chaos-based communication. This approach offers a promising framework for applications requiring high levels of data protection, with potential extensions to image encryption and other multimedia security domains. Full article

The issue of multi-switch generalized projective anti-synchronization of fractional-order chaotic systems is investigated in this work. The model is constructed using Caputo–Fabrizio derivatives, which have been rarely addressed in previous research. In order to expand the symmetric and asymmetric synchronization modes of chaotic systems, we consider modeling chaotic systems under such fractional calculus definitions. Firstly, a new fractional-order differential inequality is proven, which facilitates the rapid confirmation of a suitable Lyapunov function. Secondly, an effective multi-switching controller is designed to confirm the convergence of the error system within a short moment to achieve synchronization asymptotically. Simultaneously, a multi-switching parameter adaptive principle is developed to appraise the uncertain parameters in the system. Finally, two simulation examples are presented to affirm the correctness and superiority of the introduced approach. It can be said that the symmetric properties of Caputo–Fabrizio fractional derivative are making outstanding contributions to the research on chaos synchronization. Full article

We investigate the stochastic disruption of synchronization patterns in a system of two non-identical Rulkov neurons coupled via an electrical synapse. By analyzing the system deterministic dynamics, we identify regions of mono-, bi-, and tristability, corresponding to distinct synchronization regimes as a function of coupling strength. Introducing stochastic perturbations to the coupling parameter, we explore how noise influences synchronization patterns, leading to transitions between different regimes. Notably, we find that increasing noise intensity disrupts lag synchronization, resulting in intermittent switching between a synchronous three-cycle regime and asynchronous chaotic states. This intermittency is closely linked to the structure of chaotic transient basins, and we determine a noise intensity range in which such behavior persists, depending on the coupling strength. Using both numerical simulations and an analytical confidence ellipse method, we provide a comprehensive characterization of these noise-induced effects. Our findings contribute to the understanding of stochastic synchronization phenomena in coupled neuronal systems and offer potential implications for neural dynamics in biological and artificial networks. Full article

Dynamic criticality—the balance between order and chaos—is fundamental to genome regulation and cellular transitions. In this study, we investigate the distinct behaviors of gene expression dynamics in MCF-7 breast cancer cells under two stimuli: heregulin (HRG), which promotes cell fate transitions, and epidermal growth factor (EGF), which binds to the same receptor but fails to induce cell-fate changes. We model the system as an open, nonequilibrium thermodynamic system and introduce a convergence-based approach for the robust estimation of information-thermodynamic metrics. Our analysis reveals that the Shannon entropy of the critical point (CP) dynamically synchronizes with the entropy of the rest of the whole expression system (WES), reflecting coordinated transitions between ordered and disordered phases. This phase synchronization is driven by net mutual information scaling with CP entropy dynamics, demonstrating how the CP governs genome-wide coherence. Furthermore, higher-order mutual information emerges as a defining feature of the nonlinear gene expression network, capturing collective effects beyond simple pairwise interactions. By achieving thermodynamic phase synchronization, the CP orchestrates the entire expression system. Under HRG stimulation, the CP becomes active, functioning as a Maxwell’s demon with dynamic, rewritable chromatin memory to guide a critical transition in cell fate. In contrast, under EGF stimulation, the CP remains inactive in this strategic role, passively facilitating a non-critical transition. These findings establish a biophysical framework for cell fate determination, paving the way for innovative approaches in cancer research and stem cell therapy. Full article

In this Topic, 34 (thirty-four) papers were selected and published on the following sub-themes: Modeling and Nonlinear Systems (Contributions 1–5); Control, Synchronization, and Optimization (Contributions 6–13); Chaos and Hyperchaos (Contributions 3 and 14–20); Complex Systems (Contributions 21–25); and Applications to Engineering and Sciences (Contributions 22 and 26–32) [...] Full article

This paper presents a modified image encryption scheme based on the OTP (One-Time Pad) algorithm, consisting of chaotic synchronization and artificial neural networks (ANNs) for improved security and efficiency. The scheme uses chaotic synchronization based on feedback control to create complex and unique encryption keys. Additionally, ANNs are used to approximate time functions, creating a neural encoding key, which adds an additional layer of complexity to the encryption process. The proposed scheme integrates static, chaotic, and neural keys in a multilayer structure, providing high resistance against statistical and cryptographic attacks. The results show that the proposed methodology achieves entropy values close to the theoretical maximum, effectively destroys the correlation between pixels, and demonstrates high sensitivity to variations in the input data. The proposed scheme shows very good feasibility in terms of both security and efficiency, which gives a reliable solution for secure image transmission and storage. This is proven by a study of resistance to various crypto–graphic attacks such as brute force attack, differential attack, noise and data cut attacks, key sensitivity, and computational complexity. Full article

In this paper, we study the synchronization of dissipative quantum harmonic oscillators in the framework of a quantum open system via the active–passive decomposition (APD) configuration. We show that two or more quantum systems may be synchronized when the quantum systems of interest are embedded in dissipative environments and influenced by a common classical system. Such a classical system is typically termed a controller, which (1) can drive quantum systems to cross different regimes (e.g., from periodic to chaotic motions) and (2) constructs the so-called active–passive decomposition configuration, such that all the quantum objects under consideration may be synchronized. The main finding of this paper is that we demonstrate that the complete synchronizations measured using the standard quantum deviation may be achieved for both stable regimes (quantum limit circles) and unstable regimes (quantum chaotic motions). As an example, we numerically show in an optomechanical setup that complete synchronization can be realized in quantum mechanical resonators. Full article

A chaotic synchronization system based on two mutually injected semiconductor ring lasers (SRLs) is constructed and the synchronization performance is analyzed. First, based on the symmetric theory, three types of chaos synchronization, isochronal chaos synchronization between the same modes (ICSS), isochronal chaos synchronization between different modes (ICSD), and leader-laggard chaos synchronization between different modes (LLCSD) are identified. Then, the performance of the three types of synchronization is investigated by cross-correlation technology. The results show that, with the appropriate feedback and injection parameters, all three synchronization structures can achieve high-quality chaos synchronization. Among them, ICSS can achieve high-quality synchronization under various parameters, while ICSD and LLCSD require larger injection and feedback parameters to achieve a comparable synchronization quality. Finally, the impact of a parameter mismatch on three types of synchronization quality is studied, and the results showed that the LLCSD has a stronger robustness than ICSS and ICSD. Therefore, under larger injection and feedback parameters, LLSCD is the preferred structure for synchronization communication in SRL. The research results can provide a theoretical reference for the application of SRLs in chaotic secure communication. Full article

(1) Background: Handball is conceptualized as a complex dynamic system characterized by emergent behaviors, non-linearity, attractors, and self-organization, influenced by players’ interactions, environmental conditions, and tactical elements. This perspective emphasizes the importance of communication, adaptive strategies, and modern teaching methods like Non-linear Pedagogy for improving technical-tactical behaviors, advocating for a multidisciplinary approach to deepen its understanding. Thus, this narrative review aims to explore how modern theories and approaches can be integrated to provide a deeper understanding of handball’s complexity from a broad and multidisciplinary perspective. (2) Methods: A narrative review approach was employed to integrate key concepts such as chaos theory, self-organization, and non-linear pedagogy as they apply to the game’s technical-tactical dynamics. The methodology involved a comprehensive literature review to identify how emergent perceptual and social interactions influence collective performance. (3) Results: Findings indicate that team performance is not solely dependent on individual skills but on their capacity for synchronization, adaptation, and self-organization in response to competitive demands. Communication and internal cohesion emerged as critical factors for adjustment and autonomous decision-making, framed within Luhmann’s social systems theory. (4) Conclusions: The conclusions suggest that training methodologies should incorporate non-linear approaches that promote self-organization, adaptability, and player autonomy. This multidisciplinary perspective offers a deeper understanding of handball and highlights its applicability to other team sports, maximizing performance through an integrative analysis of social, philosophical, and communicative components. Full article

This work focuses on evaluating the behavior of analog chaos oscillators in field-programmable gate arrays (FPGAs). This work is motivated by a new approach to designing chaos-based communication systems using chaos oscillator circuits implemented in hardware in the transmitter and the mathematical models of the oscillator implemented on an FPGA in the receiver. Such a hybrid approach opens new possibilities for chaos-based modulation schemes for wireless sensor network (WSN) applications. This work brings a hybrid chaos-based communication system closer to realization by implementing the chaos oscillators on an FPGA and achieving analog–discrete and discrete–analog chaotic synchronization. First, this paper derives a model that simulates the dynamics of Vilnius and RC chaos oscillators using Euler–Cromer numerical integration in fixed-point arithmetic. The derived MATLAB model precisely describes the digital design and is thus directly transferred to VHDL. The synthesized digital design is compiled onto an FPGA chip and is then used to achieve analog–discrete and discrete–analog Pecora–Carroll chaotic synchronization. Full article

This article is devoted to the investigation of synchronization noise immunity in quadrature chaos shift keying (QCSK) communication systems and its profound impact on system performance. The study focuses on Colpitts and Vilnius chaos oscillators in different synchronization configurations, and the reliability of the system in the particular configuration is assessed using the bit error rate (BER) estimation. The research considers synchronization imbalances and demonstrates their effect on the accuracy of data detection and overall transmission stability. The article proposes an approach for optimal bit detection in the case of imbalanced synchronization and correlated chaotic signals in data transmission. The study practically shows the importance of the proposed decision-making technique, revealing that certain adjustments can significantly enhance system noise resilience. Full article

The problem of mathematical modeling and analysis of stochastic phenomena in population systems with competition is considered. This problem is investigated based on a discrete system of two populations modeled by the Ricker map. We study the dependence of the joint dynamic behavior on the parameters of the growth rate and competition intensity. It is shown that, due to multistability, random perturbations can transfer the population system from one attractor to another, generating stochastic P-bifurcations and transformations of synchronization modes. The effectiveness of a mathematical approach, based on the stochastic sensitivity technique and the confidence domain method, in the parametric analysis of these stochastic effects is demonstrated. For monostability zones, the phenomenon of stochastic generation of the phantom attractor is found, in which the system enters the trigger mode with alternating transitions between states of almost complete extinction of one or the other population. It is shown that the noise-induced effects are accompanied by stochastic D-bifurcations with transitions from order to chaos. Full article

This paper proposes a novel, practical, predefined-time control theory for chaotic system synchronization under external disturbances and modeling uncertainties. Based on this theory, a robust sliding mode surface is designed to minimize chattering on a sliding surface, enhancing system stability. Additionally, a norm-based adaptive control strategy is developed to dynamically adjust control gains, ensuring system convergence to the equilibrium point within the predefined time. Theoretical analysis guarantees predefined-time stability using a Lyapunov framework. Numerical simulations on the Chen and multi-wing chaotic Lu systems demonstrate the proposed method’s superior convergence speed, precision, and robustness, highlighting its applicability to complex systems. Full article

This study presents an innovative approach utilizing the new Shimizu–Morioka chaotic system. By integrating adaptive backstepping control with GYC partial region stability theory, we successfully achieve synchronization of a slave system with the proposed Shimizu–Morioka chaotic system. The architecture, encompassing the chaotic master system, synchronized slave system, adaptive backstepping controllers, and parameter update laws, has been implemented on an FPGA platform. Comparative analysis demonstrates that the synchronization convergence times (e1, e2, e3, and e4) are significantly reduced compared to conventional adaptive backstepping control methods, exhibiting speed enhancements of approximately 3.42, 3.55, 5.89, and 9.23 times for e1, e2, e3, and e4, respectively. Furthermore, the synchronization results obtained from continuous-time, discrete-time systems, and FPGA implementations exhibit consistent outcomes, validating the effectiveness of the proposed model and controller. Leveraging this validated synchronization framework, chaotic synchronization and secure image encryption are successfully implemented on the FPGA platform. The chaotic signal circuits are meticulously designed and integrated into the FPGA to facilitate a robust image encryption algorithm. In this system, digital signals generated by the synchronized slave chaotic system are utilized for image decryption, while the master chaotic system’s digital signals are employed for encryption. This dual-system architecture highlights the efficacy of the chaotic synchronization method based on the novel Shimizu–Morioka system for practical applications in secure communication. Full article