Search Results (1,517)

Time-reversible synchronization (TRS) of nonlinear oscillators is a recently proposed technique that ensures super-exponential convergence of dynamics between master and slave systems, which is beneficial in many real-time applications. Nevertheless, this approach has not been demonstrated in any real-time embedded system to practically verify it and quantitatively estimate its advantages. Furthermore, previous studies did not consider the application of time-reversible synchronization to a wide, practically relevant class of chaotic systems with piecewise-linear nonlinearity. To fill these gaps, in this work, we developed an FPGA-based time-reversible synchronization controller for the analog Chua circuit and its digital counterpart. To achieve complete synchronization, we first reconstructed dynamical equations of the circuit. Then, we performed a rigorous theoretical analysis of synchronization possibility between analog and digital systems by each single variable. Next, we implemented the digital model of the Chua circuit in the MyRIO-1900 FPGA using the reconstructed dynamical model and showed its capability of digital-to-analog and analog-to-digital conventional Pecora–Carroll (PC) synchronization. Then, an algorithm of time-reversible synchronization on MyRIO-1900 was tested, achieving complete synchronization at the predefined normalized RMSE level of 0.01, requiring an average of 8.0 fewer points and a median of 10.1 fewer points than the PC synchronization. Finally, we implemented a proof-of-concept version of a capacitive sensor based on the analog Chua circuit with an FPGA-based observer using PC synchronization or the TRS algorithm with a heuristic selection of a starting point. Our experiments reveal that when using the TRS algorithm, the time needed to detect a pre-selected 3% level of capacitance change is reduced by a mean factor of 4 and a median factor of 4.9 in comparison with the conventional PC synchronization. This allows for using the developed solution in applications where the synchronization rate is crucial, including chaos-based sensing, communication, and monitoring. Full article

In this paper, based on the Caputo-like delta fractional difference operator, we will present a fractional discrete model of a 4D Power System. We present an extension of the popular integer-order single-machine infinite-bus formulation to two fractional cases, one with commensurate (equal) fractional orders and another incommensurate (not equal). This extension captures long-memory effects in dynamics and thus offers a consistent mathematical description of the nonlinear behavior of power systems. The orders of the fractional models are analyzed numerically. Using time series evolution, phase-space plots, bifurcation maps, Lyapunov spectra, and the 0–1 chaos test, spectral entropy and $C_0$ complexity metrics, we identify chaotic regimes. Additionally, techniques for controlling chaos are explored to stabilize and regulate the dynamics of the system. Both the fractional formulations exhibit richer dynamical features than their integer counterparts, and for the incommensurate case, the sensitivity to the fractional variations is larger, generating complex nonlinear oscillations. The fractional discrete power system framework provides a new perspective for studying instability, the voltage collapse phenomenon, and chaotic oscillations in power engineering applications. Full article

In this study, a hybrid multi-layer scheme for reversible color image encryption is proposed, ensuring lossless reconstruction and strong cryptographic security concurrently. This method consists of three main stages. First, session-specific keys are generated using HKDF-SHA256 along with a timestamp-based mechanism to prevent replay attacks and support dynamic key management. Second, a four-layer confusion–diffusion structure is applied. It uses Gram–Schmidt orthogonal matrices, integer-based PWLCM chaotic mapping, the Hill cipher, and dynamically created S-Boxes. These operations rely on integer modular arithmetic ${\mathbb{Z}}_{256}$ and Q16.16 fixed-point precision. Finally, ChaCha20 stream encryption with HMAC-SHA256 authentication is used to secure data transmission in distributed environments. Experimental tests conducted on standard images show strong cryptographic performance, including near-ideal entropy (7.9993 bits), a significant avalanche effect ($NPCR99.6\mathrm{\%}$, $UACI33.4\mathrm{\%}$), and very low pixel correlation. The method achieves perfect lossless reconstruction and provides an effective key space $\ge 2¹²⁸$. These results confirm the suitability of the proposed scheme for secure image protection in applications requiring bit-exact recovery, such as medical imaging, digital forensics, and satellite communications. Full article

In this paper, a supply–demand–price network model incorporating a marginal feedback mechanism is proposed to characterize the evolution of market prices. Unlike classical supply–demand models, the marginal effect of excess demand, defined as the rate of change in excess demand, is explicitly introduced into the price adjustment process. As the coefficient of the marginal feedback term varies, the system exhibits rich and complex nonlinear dynamics. In particular, the model gives rise to a centrally symmetric double-wing chaotic attractor, as well as a pair of coexisting single-wing chaotic attractors. The transition routes among different dynamical regimes are systematically analyzed using phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, multistability phenomena are observed, including the coexistence of equilibrium points, limit cycles, and chaotic attractors. The corresponding basins of attraction are illustrated to reveal their intricate and interwoven structures. In addition, the emergence of endogenous chaos is investigated through both theoretical analysis and numerical simulations. Finally, the consistency between the model dynamics and real market data provides empirical evidence supporting the validity and applicability of the proposed framework. Full article

This paper investigates duopoly competition under both constant and decreasing returns to scale in a market characterized by an isoelastic demand function, where firms adjust their strategies using a gradient adjustment mechanism. To establish the stability conditions of the model, we adopt different analytical approaches depending on the type of returns to scale. Under constant returns to scale, we employ a traditional approach by deriving the closed-form solution of the Nash equilibrium and analyzing the Jacobian matrix to verify whether the moduli of all eigenvalues are less than one. In contrast, under decreasing returns to scale, we analyze the local stability of the Nash equilibrium using symbolic computation methods without deriving a closed-form solution. The results show that when firms have heterogeneous costs, the model can exhibit both period-doubling and Neimark–Sacker bifurcations under both types of returns to scale. However, when costs are homogeneous, only period-doubling bifurcations occur. Numerical simulations support these analytical results and further demonstrate the emergence of complex dynamics, including chaotic behavior. Full article

Men who have used violence against intimate partners remain an under-researched population, despite their potential to advance understanding of motivations and relational dynamics underlying such behavior. This study employed semi-structured interviews and interpretative phenomenological analysis to examine the lived experiences of five adult men with histories of partner violence. A superordinate theme, Chaotic Interpersonal and Systemic Relationships, encompassed five experiential themes describing volatile partnerships shaped by mutual vulnerabilities. Participants commonly reported trauma histories and/or antisocial traits influencing partner selection, with abuse experienced as bidirectional. Disillusionment emerged when participants perceived that the mutual nature of violence was unacknowledged, limiting their engagement in meaningful change. Although behavior change programs were often understood at a conceptual level, participants struggled to translate insight into sustained behavioral transformation. Consistent with post-traumatic growth theory, participants described developing greater personal responsibility and more constructive views of relationships over time. Greater systemic recognition of bidirectional violence, identified in the literature as a prevalent form of intimate partner violence, may strengthen the therapeutic alliance and support more nuanced etiological inquiry. Shifting systemic responses from deficit-based, gendered models toward strength-based approaches may better harness men’s capacity for more permanent positive psychological and behavioral change. Full article

With the rapid advancement of exoskeletons and rehabilitation robotics, modern healthcare increasingly demands high dynamic accuracy and reliability from medical devices. However, the dynamic response and durability of mechanical systems are greatly influenced by the inevitable existence of clearances in kinematic joints. Existing studies predominantly focus on simplified planar or spatial mechanisms, offering limited guidance for complex mechanical structures in medical applications. To address this issue, a unified modeling framework is proposed in this study to explore the nonlinear dynamic behavior and wear properties of bionic humanoid rigid mechanisms incorporating revolute joint clearances. A dynamic model that accounts for revolute joint clearances is established, employing the Lankarani–Nikravesh contact model alongside a refined Coulomb friction approach to characterize contact behavior. To characterize the wear progression between the shaft and the bushing, the Archard wear model is employed, while the system’s dynamic equations are formulated using the Lagrange multiplier approach. Systematic simulations are conducted to examine the effects of clearance size, location, and multi-clearance coupling on dynamic response and wear behavior. The results reveal that clearances at the hip joint have the most pronounced impact on system performance, tibiofemoral joint clearances exacerbate precision disturbances, and foot-end clearances considerably undermine system robustness. Increased clearance sizes and the coexistence of multiple clearances aggravate wear and induce more severe nonlinear dynamic phenomena. Phase portraits and Poincaré maps further illustrate that the system may exhibit complex or chaotic behavior under certain conditions. This study offers theoretical insights into performance degradation mechanisms in humanoid robots with joint clearances and introduces a modular “driving–mid–terminal” structure that enhances model generality, enabling its application to exoskeletons and rehabilitation devices for design optimization, service life prediction, and health monitoring. Full article

Chaotic signals commonly exhibit nonlinear and nonstationary characteristics, while noise contamination reduces signal interpretability and degrades subsequent feature extraction and dynamical analysis. To improve the stability of mode-boundary determination and mitigate reconstruction distortion, this paper proposes a hybrid denoising framework that integrates feature mode decomposition (FMD), amplitude-aware permutation entropy (AAPE), dual-tree complex wavelet transform (DTCWT), and Savitzky–Golay (SG) filtering. First, the noisy signal is decomposed into multiple mode components using FMD. Then, the AAPE of each mode is calculated to adaptively distinguish high-frequency noise-dominant modes from non-high-frequency modes. For the high-frequency noise-dominant modes, improved logarithmic threshold shrinkage is applied to the magnitudes of DTCWT complex coefficients to suppress random noise and reduce threshold-induced bias. For the non-high-frequency modes, SG filtering is employed to further attenuate residual noise while preserving local waveform structures. Finally, the processed modes are reconstructed to obtain the denoised signal. Experiments on a simulated Lorenz chaotic signal and a real-world sunspot time series demonstrate that, across different noise levels, AAPE provides more stable mode partitioning than ApEn, CC, and CMSE. Moreover, under Gaussian white noise, Poisson noise, and uniform noise, the proposed method generally achieves a higher output signal-to-noise ratio (SNR) and a lower root mean square error (RMSE) than WT, CEEMD, EEMD, CEEMDAN+LMS, and VMD, while also yielding better performance in phase-space reconstruction and temporal-detail recovery. These results verify the effectiveness and practical applicability of the proposed method for chaotic signal denoising. Full article

With the rapid growth of digital image transmission, ensuring data security has become increasingly important. However, existing chaos-based image encryption algorithms often suffer from insufficient chaotic randomness and weak integration between chaotic dynamics and encryption mechanisms. To address these issues, a novel image encryption scheme based on a two-dimensional hyperbolic–exponential Sine–Logistic map (2D-HESLM) is proposed. A Sierpiński carpet-inspired scrambling strategy and a cascaded diffusion mechanism are designed to enhance permutation and diffusion performance based on the 2D-HESLM. The experimental results show that the information entropy value is 7.9980, while NPCR and UACI are approximately averaged 99.6147% and 33.4672%, respectively, with correlation coefficients close to zero. These results demonstrate the effectiveness and security of the proposed scheme. Full article

Chaotic behavior in power systems that are integrated with permanent-magnet synchronous generators (PMSGs) poses a significant threat to stability and security. Existing control methods often suffer from slow convergence, reliance on precise system models, or the inability to guarantee convergence within a predefined time. To address these issues, this paper develops a predefined-time synchronization control scheme for chaotic PMSG systems under unknown nonlinearities and external disturbances. First, an adaptive neural network with variable exponent coefficients is constructed to approximate unknown system dynamics online. Second, a predefined-time stability criterion is established, ensuring global convergence of synchronization errors within a user-specified time, independently of initial conditions. Third, the proposed controller achieves superior disturbance rejection without requiring prior knowledge of disturbance bounds. Numerical simulations demonstrate that the proposed method outperforms conventional finite-time control in convergence speed, control smoothness, and robustness to parameter variations—offering a practical and theoretically guaranteed solution for enhancing the stability of PMSG-based power systems. Full article

While general network dynamics have been extensively modeled using stochastic methods, the emergence of dense Internet of Things (IoT) ecosystems demands a more specialized analytical framework. IoT environments are characterized by extreme non-linearity and sensitivity to initial conditions, where traditional models often fail to account for chaotic latency and packet loss. This paper introduces a specialized approach that integrates Chaos Theory with the innovative paradigm of Vibe Coding—an AI-assisted development and analysis methodology that allows for the ‘encoding’ and interpretation of the dynamic ‘vibe’ or signature of network fluctuations in real-time. By categorizing network behavior into four distinct scenarios (quiescent, perturbed, attacked, and perturbed–Attacked), the proposed framework utilizes deep learning to transform chaotic signals into actionable intelligence. Our findings demonstrate that this specialized synergy between chaos analysis and Vibe Coding provides superior classification of adversarial threats, such as DoS and injection attacks, fostering intelligent native security for next-generation IoT infrastructures. Full article

In response to the problem that sensors cannot be directly installed at key local positions on the surface of ship hull structures during the transient strong shock process of underwater explosions due to spatial constraints or large plastic deformations, this paper investigates the chaotic-like nonlinear transient behavior of structural dynamic response systems under strong shock and proposes a key position structural response reconstruction method based on dynamic inversion. Since the structural response under a transient strong shock exhibits significant non-stationarity and nonlinearity, signals from neighboring measurement points cannot directly characterize the dynamic behavior at key positions. Therefore, the shock response signals are discretized in both time and space dimensions. The phase space reconstruction method is employed to characterize the motion trajectory of acceleration responses in a two-dimensional phase space, establish mapping functions for system motion evolution, and use their control parameters to characterize the system’s nonlinear dynamic behavior. Furthermore, based on the spatiotemporal dynamic equations, a spatiotemporal coupled mapping model for spatial state points is established to achieve the theoretical inversion of acceleration responses at key positions. This method provides theoretical support for analyzing the dynamic characteristics of structures at key positions under strong shock environments, characterizing the shock environment, and assessing and designing equipment for shock safety. However, the current validation is based on high-fidelity numerical simulations rather than physical prototype tests; therefore, the predictive capability of this method in actual physical environments requires further validation through subsequent physical model tests. Full article

To address the challenges of low-carbon economic optimization and collaborative management for multiple Virtual Power Plants (VPPs), this paper proposes a low-carbon economic optimization and collaborative management method based on a Stackelberg game framework. Firstly, a Stackelberg game model is constructed with the Distribution System Operator (DSO) as the leader and multiple VPPs as followers. The leader (DSO) guides the followers’ behavior through dynamic pricing strategies to maximize its own utility. Meanwhile, the followers (VPPs) develop energy management strategies to minimize their individual costs, taking into account factors such as energy transaction costs, fuel costs, carbon trading costs, operation and maintenance (O&M) costs, compensation costs, and renewable energy generation revenues. Furthermore, the strategy spaces of all participants are defined, and an optimization model is established subjected to constraints including energy balance, energy storage operation, power conversion, and flexible load response. The CPLEX solver and Nonlinear-based Chaotic Harris Hawks Optimization (NCHHO) algorithm are employed to solve the proposed game model. Simulation results demonstrate that the proposed method effectively facilitates collaboration between the DSO and multiple VPPs. While ensuring the safe operation of the system, it balances the profit between the DSO and VPPs, and incentivizes renewable energy consumption and indirect carbon reduction, thereby validating the effectiveness and superiority of the method and providing reliable technical support for the low-carbon collaborative operation of multiple VPPs. Full article

This paper proposes a novel four-dimensional strongly dissipative nonlinearly coupled hyperchaotic system, investigates its dynamical characteristics, and demonstrates its applicability through Deoxyribonucleic Acid (DNA)-encoded RGB image encryption. First, a four-dimensional nonlinearly coupled hyperchaotic system with strong dissipativity is constructed. Nonlinear dynamics analysis methods, including phase trajectory diagrams, Lyapunov exponent spectra, and bifurcation diagrams, are employed to thoroughly reveal the system’s complex dynamical evolution mechanisms. The analysis indicates that the system not only possesses a wide range of chaotic parameters but also exhibits rich phenomena of multiple coexisting attractors, demonstrating a high degree of multistability. This characteristic offers potential advantages for image encryption, as it increases the diversity of dynamical behaviors and enhances sensitivity to initial conditions. The physical realizability of the chaotic behavior is further verified through an analog circuit implementation. Consequently, the system supports the design of encryption algorithms with larger key spaces, stronger resistance to phase space reconstruction, and improved pseudo-randomness, making it particularly suitable for applications with extremely high security requirements. Subsequently, leveraging the highly random chaotic sequences generated by this system, combined with various DNA coding rules and operations, the RGB image components are scrambled and diffused for encryption. Security analysis demonstrates that the algorithm effectively passes examinations across multiple dimensions, including histogram analysis, information entropy, adjacent pixel correlation, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), and The Peak Signal-to-noise Ratio (PSNR). It achieves favorable encryption results, significantly enhances image resistance against attacks, and provides a reliable technical solution for the secure transmission of remote sensing and military images. Full article

To address the inherent nonlinearity and time-varying dynamics of tractor steer-by-wire (SbW) hydraulic systems, as well as the inadequacies of empirical PID tuning in achieving rapid dynamic response and high tracking accuracy during headland maneuvers, continuous steering, and stochastic field operations, this study proposes an Improved Sparrow Search Algorithm (ISSA)-PID control strategy. Initially, an SbW hydraulic test bench was established, and an asymmetric dynamic transfer function model of the steering system was identified utilizing the Nelder–Mead simplex method. To overcome the susceptibility of the conventional Sparrow Search Algorithm (SSA) to local optima entrapment and its insufficient population diversity, the Circle chaotic map was employed to enhance the initial population distribution. Furthermore, an adaptive t-distribution mutation strategy was incorporated to coordinate global exploration and local exploitation, facilitating the optimization of the PID parameters. Hardware-in-the-loop (HIL) bench tests were conducted to evaluate the performance of the different control algorithms. With the proposed ISSA-PID controller, under step response conditions, accounting for the inherent dynamics of the asymmetric steering cylinder, the response times for left and right turns were reduced to 0.77 s and 0.98 s, respectively. During random signal tracking tests that emulate stochastic field operations, the average tracking error was minimized to 0.75°, with a maximum deviation restricted to 1.27°. These results demonstrate that the proposed ISSA-PID strategy addresses parameter tuning challenges, improving control precision and dynamic response. Consequently, it offers a practical control strategy for tractor SbW hydraulic systems. Full article