Search Results (193)

This paper investigates the dynamic behavior of a Kolmogorov-type permanent-magnet synchronous generator for wind power systems. Firstly, the chaotic model of the salient-pole permanent-magnet synchronous generator is derived and subsequently transformed into a Kolmogorov-type system. Secondly, by analyzing the derived Kolmogorov system, the system’s stability is established, and the boundary ellipsoid of the chaotic attractor is determined via the Casimir energy function. Thirdly, the analysis focuses on the mechanisms leading to chaos, including period-doubling bifurcation and the onset of double Hopf bifurcation. Finally, the basins of attraction associated with the coexisting static attractors are determined to characterize their long-term dynamical behavior. The analytical results show good agreement with the numerical simulations. Full article

Wireless sensor networks (WSNs) have increasing demand on lightweight, efficient, and secure encryption techniques for devices with limited resources, since traditional algorithms require high computation which make them impractical. This preliminary study presents an encryption algorithm based on chaos designed for transmitting short data, using the Lorenz system and Euler’s method for computation. It is combined with a synchronization model based on data array. It inserts iteration parameters within the ciphertext to ensure consistent key reproduction while decrypting. Within the broader context of e-health data streams, encryption efficiency is critical: continuous ECG signals generate large volumes of data that challenge real-time secure transmission, whereas individual blood pressure readings are far smaller and lightweight. While this work delimits its scope to short, low-power transmissions, simulations and hardware implementation on an nRF chip using the Enhanced ShockBurst (ESB) protocol demonstrated efficiency, with the lowest encryption speed of 0.154 ms for a 1-byte payload. Security analysis using the NIST Statistical Test Suite confirmed high statistical randomness of the generated keystream, and theoretical key-space analysis supports robustness. By focusing on short-stream encryption in preliminary form, the scheme contributes toward inclusive secure communication technologies for resource-constrained IoT healthcare systems and diverse user populations. Full article

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

As nuclear energy expands, nuclear emergency response systems increasingly exhibit strong human–machine–environment (H–M–E) coupling, long-duration operations, and multi-department coordination, in which minor disturbances can be amplified by feedback loops into cascading failures and loss of situational control. To address the inability of conventional static and linear methods to represent dynamic risk evolution and chaotic uncertainty, this study proposes an integrated “risk network–chaotic evolution–synchronization control” framework. Based on 12-year-old on-site comprehensive drill reports from a Chinese nuclear power base, we construct a directed H–M–E risk network in a semi-quantitative, qualitative–quantitative manner and identify critical nodes using a composite betweenness–PageRank risk metric. We further abstract the system into a three-dimensional nonlinear coupled dynamical model; phase portraits, Lyapunov exponents, and bifurcation analysis confirm threshold effects, period-doubling routes, and chaotic attractors, revealing nonlinear amplification under strong coupling. Finally, an adaptive chaotic synchronization controller driven by network coupling strength is designed. Simulations show all strategies suppress chaos and achieve synchronization, while the machine-dominated strategy offers the best speed–energy trade-off for emergency resource allocation. Full article

This paper investigates the dynamics of a permanent magnet synchronous motor (PMSM) and controls its chaotic speed behavior using the synergetic control technique (SCT). The model includes electrical dynamics in the dq frame and mechanical speed dynamics, with a scalar parameter $\gamma$ capturing cross-coupling effects. The equilibrium structure and local stability properties of the PMSM are analyzed. For zero input voltages and zero load torque, the system exhibits a pitchfork-type bifurcation in the electrical–mechanical equilibrium as $\gamma$ crosses a critical value. Explicit expressions are derived for all equilibria, and their stability is characterized using eigenvalue analysis and the Routh–Hurwitz criterion, and a secondary loss of stability via a Hopf-type mechanism is identified. The case of nonzero input voltages with zero load torque is also discussed. Numerical simulations confirm the analytical results and highlight the parameter regions that admit stable operation. Bifurcation diagrams show the different PMSM behaviors as the parameter $\gamma$ varies. For a certain interval of $\gamma$, the PMSM speed undergoes chaotic oscillations. The SCT is introduced to control the chaos. Macro variables are chosen to design the SCT. The derived SCT is implemented to eliminate the chaotic speed. The controller provides good performance in suppressing the chaos. The controller is tested under sudden reference speed change where the controller gets the new reference speed accurately. It is also evaluated under sudden and sinusoidal load torque variations. Full article

The proliferation of Internet of Things (IoT) devices and services creates not only significant benefits but also new security threats. Classical information encryption techniques are not suitable for resource-constrained edge modules, thereby generating the demand for lightweight and efficient data protection algorithms. This work presents a novel dynamical parameter estimation scheme for chaotic oscillators, applied to physical-layer authentication (PLA). The proposed approach relies on the receiver’s capability to estimate a selected parameter of the transmitter’s oscillator determined by circuit configuration from the received chaotic signal using a locally synchronized oscillator, thereby enabling secure authentication based on a hardware-encoded identifier. The scheme is intended to complement a chaos-based wireless sensor network (WSN) architecture, where sensor nodes (SNs) implement analog chaotic oscillators, and the gateway operates discrete-time models. The Vilnius chaotic oscillator was chosen to validate the proposed PLA scheme. A rigorous bifurcation analysis of analytical, SPICE and discrete oscillator models was first conducted to identify parameter regions that preserve chaotic dynamics, establishing correspondence between models to guarantee the feasibility of parameter estimation across implementations. The digital realization of the parameter estimator demonstrated accurate and stable operation, with a small and nearly constant estimation relative error not exceeding 1.01%. Key performance metrics were analyzed, including estimation time, precision, and noise robustness. A tradeoff between estimation speed and accuracy was identified, particularly under noisy channel conditions. Finally, the influence of the receiver’s native oscillator parameter on distinguishable transmitter parameter ranges was demonstrated, highlighting the configurability and security potential of the proposed system against unauthorized transmissions. Full article

To improve the safety of road transportation of Spent Nuclear Fuel (SNF), this paper proposes a novel approach for risk identification and chaotic synchronous control in SNF road transportation systems. Firstly, a dynamic risk evolution model for the road transportation of SNF is developed by analyzing the nonlinear interactions among vehicles, environmental conditions, and human factors using complex network analysis and nonlinear dynamics. Secondly, an enhanced K-shell decomposition method is applied to identify key risk nodes and assess the relative importance of different risk factors, providing a basis for targeted risk control. Finally, a chaotic synchronization control strategy based on Lyapunov stability is proposed to suppress risk divergence and restore system stability. Three targeted control schemes are evaluated by varying the control gain coefficients across the ‘Vehicle–Environment–Human’ dimensions. Simulation results indicate that the strategy prioritizing environmental and human risk control yields the fastest convergence, significantly outperforming vehicle-centric approaches. The results show that prioritizing both environmental and human-factor control is most effective for suppressing chaotic divergence. This provides a solid quantitative basis for the strategic shift from passive defense to active environmental warning, thereby significantly optimizing the dynamic risk management of the SNF transportation system. Full article

In this paper, a fractional-order discrete map with a hyperbolic sine function has been proposed and studied. Firstly, the basic characteristics of the map in integer-order case are studied theoretically and numerically. Secondly, dynamics of the map are investigated via numerical simulations. Attractors and bifurcation diagram spectrums are given when a parameter is varied. Furthermore, the map with the Caputo fractional difference operator has been studied. The chaotic attractors in commensurate-order and incommensurate-order cases are shown. For the characteristics of hyperbolic sine function, the chaotic attractors with different structures for the map can be obtained. It can be concluded that the map has rich dynamics in integer-order and fractional-order cases. Finally, stabilization and adaptive synchronization of the fractional-order map are realized by designing suitable controllers, respectively. Numerical results are used to demonstrate the effectiveness of the controllers for the map. Full article

Food supply chains play a critical role in advancing sustainability within today’s food systems. In this work, we construct a differential equation-based model with a four-layer supply chain framework that captures the intricate relationships among producers, manufacturers, distributors, and retailers while considering resource optimization, waste minimization, and supply–demand equilibrium. To better understand and predict supply chain behavior, we perform a series of model analyses. By applying chaos theory, we analyze the system’s equilibrium states and evaluate their local stability. Our findings reveal that manufacturers and retailers encounter significant difficulties when the system shifts into chaotic behavior. This can be made worse by future uncertainties. This entails formulating tailored strategies to mitigate risks. Hence, we design a set of nonlinear feedback control strategies to synchronize two chaotic supply chain networks. Theoretical validity is established using Lyapunov theory. Our simulation results confirm that the proposed strategy can eliminate synchronization errors. Furthermore, it allows for swift alignment and coordination between the networks. Overall, this synchronization method is both effective and easy to implement for managing risks and enhancing sustainability in food supply chains affected by chaotic dynamics. Full article

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

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

Financial stability in interconnected markets is increasingly challenged by nonlinear interactions that amplify local disturbances into systemic crises. This study models a financial system as a complex network of coupled chaotic nodes, where each node represents a nonlinear macroeconomic subsystem governed by endogenous feedback dynamics. In contrast to traditional centralized interventions, a pinning control strategy is proposed to stabilize a network through selective control of a small subset of influential nodes. Numerical simulations show how local crises propagate through coupling links, generating systemic instability, and how the proposed impulsive control scheme effectively suppresses chaos and restores synchronization across an entire network. Results highlight the efficiency of localized interventions for achieving global stability, offering new theoretical insights into mechanisms of financial correlation and design of control-based resilience strategies for complex economic systems. Full article

This paper investigates a discrete-time compartmental model for computer virus propagation. The model classifies computers into susceptible, latent, and breaking-out states, with nonlinear dynamics driven by infection, recovery, and breakout processes. Stability is analyzed using the basic reproduction number $R_0$, and chaotic behavior is demonstrated through phase portraits, bifurcation diagrams, and maximum Lyapunov exponents. To further characterize complexity, the $C_0$ complexity measure is computed, confirming the richness of the chaotic regime. In addition, control strategies are designed to stabilize the dynamics, and a master–slave synchronization scheme is proposed and validated. Numerical simulations highlight both the complexity and controllability of the system, underscoring its relevance for understanding and mitigating the propagation of computer viruses. Full article

The study of economic maps has consistently attracted researchers due to their rich dynamics and practical relevance. A deeper understanding of these systems enables the development of more effective control strategies. In this work, we examine the influence of the fractional order $\upsilon$ with the Caputo fractional difference on an economic market map. The primary contribution is the comprehensive analysis of how both commensurate and incommensurate fractional orders affect the stability and complexity of the map. Numerical investigations, including phase portraits, largest Lyapunov exponents, and bifurcation analysis, reveal that the system undergoes a cascade of period-doubling bifurcations before transitioning into chaos. To further characterize the dynamics, complexity is evaluated using the 0–1 test and $C_0$ complexity, both confirming chaotic behavior. Furthermore, two-dimensional control schemes are introduced and theoretically validated to both stabilize the chaotic economic market map and achieve synchronization with a combined response map. The theoretical and numerical results are validated through MATLAB 2016 simulations. Full article

This paper introduces an enhanced five-dimensional Chaotic Supply Chain Model (5DCSCM) by incorporating a transport lag variable into a previously established four-dimensional model. The newly added differential equation in the transit dynamics of the supply chain model captures the inherent lag between customer demand and the physical response in transportation, modeled as a first-order transport lag system. Through comprehensive numerical simulations, the influence of various system parameters—including customer demand rate, delivery efficiency, information distortion, contingency reserve, safety stock, and transportation lag—are examined. The study utilizes bifurcation diagrams and a Lyapunov Exponent (LE) to investigate tran-sitions between periodic and chaotic behavior. Additionally, the model is extended with offset boosting control, allowing for controlled amplitude adjustment without altering the underlying chaotic dynamics. Offset boosting control (OBC) is useful in chaotic supply chain systems because it stabilizes inventory and order fluctuations by counter-acting the amplification of small disturbances, reducing the bullwhip effect, and im-proving overall system reliability and responsiveness. As an application, integral sliding mode control (ISMC) technique has been applied to achieve complete synchronization between a pair of the 5DCSCM. Synchronization based on ISMC is useful in chaotic supply chain systems because it ensures robust coordination between different tiers, suppresses chaos-induced fluctuations, and maintains stable inventory and order patterns even under disturbances and uncertainties. Full article