Search Results (45)

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

This paper presents the design and multi-domain evaluation of three chaos-based excitation strategies for brushless DC (BLDC) motor drives implemented using Chua circuit-generated deterministic chaotic signals injected at three distinct control points: the PWM duty cycle, the commutation sequence, and the current feedback loop. A systematic design methodology is established for each injection architecture, including signal normalization, amplitude parameterization, and injection point characterization, evaluated across the electromagnetic, thermal, mechanical, and acoustic domains through MATLAB (R2024a) simulation and physical test stand validation. PWM injection produces controlled spectral dispersion with 5–7% speed reduction and a 10–15 dB SNR decrease, making it the recommended design choice for acoustic signature masking in stealth UAV applications. Commutation injection achieves severe system destabilization with speed reduction exceeding 56% and SNR losses greater than 30 dB, establishing it as a design tool for accelerated stress testing and fault emulation. Current feedback injection delivers a balanced excitation profile with 12–20% efficiency loss and 16–30% SNR reduction, making it suitable as a design method for online parameter identification and adaptive control development. This study establishes the first multi-domain comparative design framework for application-specific selection of chaos excitation strategies in BLDC drives, supported by nonparametric statistical validation and experimental acoustic confirmation, providing drive engineers with quantitative selection criteria across four physical domains. Full article

Bounds for positive definite sets such as attractors of dynamic systems are typically characterized by Lyapunov-like functions. These Lyapunov functions and their time derivatives must satisfy certain definiteness conditions, whose verification usually requires considerable experience. If the system and a Lyapunov-like candidate function are polynomial, the definiteness conditions lead to Boolean combinations of polynomial equations and inequalities with quantifiers that can be formally solved using quantifier elimination. Unfortunately, the known algorithms for quantifier elimination require considerable computing power, meaning that many problems cannot be solved within a reasonable amount of time. In this context, it is particularly important to find a suitable mathematical formulation of the problem. This article develops a method that reduces the expected computational effort required for the necessary verification of definiteness conditions. The approach is illustrated using the example of the Chua system with cubic nonlinearity. Full article

This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry—most notably sign-reversal invariance in the Lorenz system and Chua’s circuit models and a coordinate-wise sign pattern in the Lorenz–Haken equations—which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design. Full article

With the growing demand for secure image communication, effective encryption solutions are critical for safeguarding visual data from unauthorized access. The substitution box (S-box) in AES (Advanced Encryption Standard) is critical for ensuring nonlinearity and security. However, the static S-box used in AES is vulnerable to algebraic attacks, side-channel attacks, and so on. This study offers a novel Lorenz key and Chua key-based Reversible Substitution Box (LCK-SB) for image encryption, which takes advantage of the chaotic behavior of the Lorenz and Chua key systems to improve security due to nonlinear jumps and mixed chaotic behavior while maintaining optimal quantum cost, area, and power. The suggested method uses a hybrid Lorenz and Chua key generator to create a highly nonlinear and reversible S-box, which ensures strong confusion and diffusion features. The performance of the LCK-SB approach is examined on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) platforms, and the findings show that quantum cost, delay, and power are decreased by 97%, 74.6%, and 35%, respectively. Furthermore, the formal security analysis shows that the suggested technique efficiently resists threats. The theoretical analysis and experimental assessment show that the suggested system is more secure for picture encryption, making it suitable for real-time and high-security applications. Full article

Sudden cardiac death (SCD) represents a critical public health challenge, emphasizing the need for predictive techniques that model complex physiological dynamics. Studies indicate that the “V-trough” pattern in sympathetic nerve activity (SNA) could act as an early indicator of potentially fatal cardiac events, which can be effectively modeled using a modified version of Chua’s chaotic system, incorporating the variables of heart rate (HR), SNA, and blood pressure (BP). This paper introduces a Chua circuit with delay, and proposes a novel control design technique based on Lurie-type control systems theory combined with mixed-sensitivity ${\mathcal{H}}_{\infty }$ ($S/KS/T$) methodology. The proposed controller enables precise regulation of HR in Chua’s circuit, both with and without delay, paving the way for the development of advanced devices capable of preventing SCD. Furthermore, the developed theory allows for the project of robust controllers for delayed Lurie systems within the single-input–single-output (SISO) framework. The presented theoretical framework, supported by numerical simulations, demonstrates the effectiveness of the conceptualization, marking a considerable advance in the understanding and early intervention of SCD through robust and nonlinear control systems. Full article

Understanding the intricate and dynamic nature of brain disorders, such as epilepsy, Parkinson’s disease, and schizophrenia, presents a formidable challenge due to their inherent chaotic properties, which defy conventional analytical approaches. In response to this challenge, our research introduces a groundbreaking methodology aimed at simulating the chaotic behavior characteristic of these neurological conditions using advanced electrical circuit models. By conceptualizing the interactions among neurons and synapses as electrical components within our model, we endeavor to unravel the complex underlying mechanisms driving these disorders. Leveraging insights from chaos theory and drawing upon the rich toolkit of electrical engineering, our simulation framework offers a novel perspective on the ways in which disruptions within neural circuits manifest as pathological states, shedding light on the intricate dynamics of brain diseases. Through rigorous numerical simulations and thorough analysis, we illustrate the efficacy of our approach in deciphering the chaotic dynamics inherent in these disorders, thus laying the foundation for the development of innovative therapeutic interventions. Furthermore, our research underscores the paramount importance of fostering interdisciplinary collaboration between the fields of neuroscience and electrical engineering; as such, synergistic partnerships hold the key to unlocking new frontiers in understanding and effectively treating complex neurological disorders, thus paving the way for improved patient outcomes and enhanced quality of life. Full article

This paper presents a novel dynamic adaptive event-triggered mechanism (DAETM) for addressing actuator saturation in leader–follower fractional-order nonlinear multi-agent networked systems (FONMANSs). By utilizing a sector-bounded condition approach and a convex hull representation technique, the proposed method effectively addresses the effects of actuator saturation. This results in less conservative linear matrix inequality (LMI) criteria, guaranteeing asymptotic consensus among agents within the FONMANS framework. The proposed sufficient conditions are computationally efficient, requiring only simple LMI solutions. The effectiveness of the approach is validated through practical applications, such as synchronous generators within a FONMANS framework, where it demonstrates superior performance and robustness. Additionally, comparative studies with Chua’s circuit system enhance the robustness and efficiency of control systems compared to existing techniques. These findings highlight the method’s potential for broad application across various multi-agent systems, particularly in scenarios with limited communication and actuator constraints. The proposed approach enhances system performance and provides a robust, adaptive control solution for dynamic and uncertain environments. Full article

In this paper, an incommensurate fractional-order chaotic system is established based on Chua’s system. Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different fractional orders are studied. Meanwhile, the incommensurate system parameters and initial values are used as variables to study the dynamic characteristics of the incommensurate system. It is found that there are rich coexistence bifurcation diagrams and coexistence Lyapunov exponent spectra which are further verified with the phase diagrams. Moreover, a special dynamic phenomenon, such as chaotic degenerate dynamic behavior, is found in the incommensurate system. Secondly, for the feasibility of practical application, the equivalent analog circuit of incommensurate system is realized according to fractional-order time–frequency frequency domain algorithm. Finally, in order to overcome the limitation that the convergence time of the finite-time synchronization control scheme depends on the initial value, a fixed-time synchronization control scheme is proposed in the selection of synchronization control scheme. The rationality of this scheme is proved by theoretical analysis and numerical simulation. Full article

The objective of this work was to design and implement a system based on reconfigurable hardware as a study tool for the synchronization of chaotic circuits. Mathematical models were established for one circuit, two synchronized, and multiple synchronized Chua circuits. An ordinary differential equation solver was developed applying Euler’s method using the Verilog hardware description language and synthesized on a Spartan 3E FPGA (Field-Programmable Gate Array) equipped with a 32-bit RISC processor, 64 MB of DDR SDRAM, and 4 Mb of PROM. With a step size of 0.005 and a total of 10,000 iterations, the state equations for one and three Chua circuits were solved at a time of 0.2 ms and a frequency of 50 Mhz. The logical resources used by the system did not exceed 4%. To verify the operation, a numerical simulation was carried out using the Octave V9.1.0 calculation software on an Intel(R) Core i7-9750H CPU 2.59 GHz computer, obtaining the same results but in a time of 493 ms and 3.177 s for one and three circuits, respectively. Full article

This study explores memristor-based true random number generators (TRNGs) through their evolution and optimization, stemming from the concept of memristors first introduced by Leon Chua in 1971 and realized in 2008. We will consider memristor TRNGs coming from various entropy sources for producing high-quality random numbers. However, we must take into account both their strengths and weaknesses. The comparison with CMOS-based TRNGs will serve as an illustration that memristor TRNGs stand out due to their simpler circuits and lower power consumption— thus leading us into a case study involving electroless YMnO₃ (YMO) memristors as TRNG entropy sources that demonstrate good security properties by being able to produce unpredictable random numbers effectively. The end of our analysis sees us pinpointing challenges: post-processing algorithm optimization coupled with ensuring reliability over time for memristor-based TRNGs aimed at next-generation security applications. Full article

We found that a second-order ideal memristor [whose state is the charge, i.e., $\mathit{x}=q$ in $\mathit{v}=\mathit{R}\left(\mathit{x},\mathit{i},\mathit{t}\right)\mathit{i}$] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world? Full article

Chua’s circuit is a well-established model for studying chaotic phenomena and is extensively implemented in fields like encrypted communication. However, a traditional Chua’s circuit has large volume, high component precision requirements and limited adjustable parameter range, which are not conducive to application. In order to solve these problems, we propose an improved implementation of Chua’s circuit on an active inductor and non-autonomous system. First, we adopt the strategy of using active inductors instead of traditional passive inductors, achieving the miniaturization of the circuit and improving the accuracy of inductance. In addition, we present the theory of substituting non-autonomous systems for classical autonomous systems to reduce the requirements for the accuracy of components and improve the robustness of the circuit. Lastly, we connect the extension resistor in parallel with Chua’s diode to optimize circuit structure, thereby increasing the range of the adjustable parameter. Based on the three improvements above, experiments have shown that the average maximum error tolerance of components of our improved design has been increased from 1.88% to 7.38% when generating a single vortex, and from 4.73% to 12.61% when generating a double vortex, compared with the traditional Chua’s circuit. The range of the adjustable parameter has been increased by 195.83% and 36.98%, respectively, when generating a single vortex and double vortex. In summary, our improved circuit is more practical than the traditional Chua’s circuit and has good application value. Full article

In this paper, we present a fully integrated circuit without inductance implementing Chua’s chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain–bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm², and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size. Full article

This paper introduces a new 3D chaotic attractor in a gene regulatory network. The proposed model has eighteen parameters. Formulas for characteristic numbers of critical points for three-dimensional systems were considered. We show that the three equilibrium points of the new chaotic 3D system are unstable and deduce that the three-dimensional system exhibits chaotic behavior. The possible outcomes of this 3D model were compared with the results of the Chua circuit. The bifurcation structures of the proposed 3D system are investigated numerically, showing periodic solutions and chaotic solutions. Lyapunov exponents and Kaplan-Yorke dimension are calculated. For calculations, the Wolfram Mathematica is used. Full article