Chaos Synchronization Research Articles

Firing modes and predefined-time chaos synchronization of novel memristor-coupled heterogeneous neuron

Firing modes and predefined-time chaos synchronization of novel memristor-coupled heterogeneous neuron

STUDY ON CHAOS CONTROL OF FRACTIONAL-ORDER UNIFIED CHAOTIC SYSTEM

This paper focuses on synchronization control of the fractional-order unified chaotic system. First, the stability of equilibria is analyzed by the Routh–Hurwitz criteria. Then, three different controllers are designed to achieve chaos synchronization of the drive-response unified system. Further, the impact of the fractional order on the synchronization performance is illustrated. Numerical simulations are carried out to verify the feasibility of theoretical analysis.

High-speed secure key distribution based on interference spectrum-shift keying with signal mutual modulation in commonly driven chaos synchronization

The secure key generation and distribution (SKGD) are unprecedentedly important for a modern secure communication system. This paper proposes what we believe to be a novel scheme of high-speed key distribution based on interference spectrum-shift keying with signal mutual modulation in commonly driven chaos synchronization. In this scheme, delay line interferometers (DLI) are utilized to generate two low-correlation interference spectra from commonly driven synchronous chaos, and then a 2 × 2 optical switch can effectively change the relationship between the two interference spectra in post-processing by shifting the states of the switch. The signals then undergo electro-optic nonlinear transformation through a hardware module, which includes a signal mutually modulating module (SMMM) and a dispersion component. This optimization significantly enhances the entropy source rate of synchronized chaos from both legitimate users. Moreover, thanks to the introduction of DLIs and electro-optic nonlinear transformation module, the key space of the proposed scheme is remarkably improved. In comparison to traditional chaotic drive-response architectures, the scheme effectively suppresses residual correlation. A 6.7 Gbit/s key distribution rate with a bit error rate below 3.8 × 10−3 is experimentally demonstrated over a 40 km single-mode fiber (SMF).

Josephson junction oscillator embedded in the microcontroller: Pseudo-random number generation and combination synchronization

Dynamical scrutiny of the resistive capacitive inductive shunted Josephson junction (JJ) oscillator (RCLSJJO), microcontroller realization, pseudo-random number generation (PRNG) and combination synchronization are achieved in this paper. Numerical probing led to the establishment that the RCLSJJO is characterized by regular behaviors, bistable periodic-2-oscillations, periodic bursting characteristics and various shapes of chaotic dynamics. Thereafter, the vast dynamical characteristics obtained theoretically are realized by the microcontroller realization with qualitative agreements. Moreover, a chaos-based PRNG is designed by using chaotic RCLSJJO and linear feedback shift register (LFSR) as post-processing unit. Satisfactory results are obtained from the NIST 800–22 test suite and the randomness of binary data generated from the proposed RCLSJJO-based PRNG is confirmed for chaos-based digital applications. Lastly, the combination chaos synchronization of two drive and one response RCLSJJO is proven thanks to the theoretical analysis.

Multi-dimensional opinion chaos synchronization based on multi-layer complex networks

Abstract In complex networks, the interactions of opinions are significantly affected by network structure. Moreover, multi-layer networks, which contain multiple subsystems and different types of interactions, are considered to have a stronger ability to simulate various real-world systems than traditional single-layer complex networks. Based on this motivation, this article attempts to show how to achieve complete synchronization of multi-dimensional opinions in a multi-layer network topology where the opinions of nodes have Rössler chaotic dynamics. A first step in investigating the synchronization of multi-layer complex networks is to propose a multi-dimensional opinion evolution model. In this article, the multi-layer complex network model combining the Rössler oscillation system is built, which provides us a tool for insight into the nodes complexity in multi-layer networks. Furthermore, a general criterion for globally exponentially asymptotic synchronization of multi-layer complex networks is provided using multiple Lyapunov stability theories. We illustrate the reliability of the model and the correctness of the criterion by Runge-Kutta (RK4) simulation. These findings shed new light on some interesting phenomena in society and help decision-makers predict the prevalence of hot topics and public opinions.

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Multi-Wavelength Broadband Chaos Generation and Synchronization Using Long-Cavity FP Lasers

Simultaneous generation and synchronization of multiple broadband laser chaos with different wavelengths are numerically demonstrated by using long-active-cavity Fabry-Perot (LC-FP) semiconductor lasers based on multi-mode beating effect. Simulation results show that the LC-FP laser under simple optical feedback can produce broadband chaos with a bandwidth up to 37 GHz with an active cavity length of about 1500um. Furthermore, common-signal-induced chaos synchronization is predicted. Driven by a common chaos from the optical-feedback LC-FP laser, two response LC-FP lasers can reach broadband chaos synchronization with a correlation coefficient beyond 0.98. Meanwhile, the drive-response correlation is low at around 0.4. More interestingly, by optical filtering, parallel multiple broadband chaotic signals at different wavelengths are obtained with bandwidths exceeding 25 GHz and cross-correlation values lower than 0.2. The chaos synchronization keeps for the identical wavelengths. This work will pave a way for increasing capacity of chaos communication.

Dynamical analysis and synchronization control of flux-controlled memristive chaotic circuits and its FPGA-Based implementation

This paper focuses on addressing the synchronization control problem of memristive chaos through the investigation of a single feedback controller strategy. Our objective is to deploy this strategy on field-programmable gate arrays (FPGA) with the aim of bolstering the security and reliability of memristive chaotic synchronization control. Concurrently, we seek to enhance system performance and fulfill the diverse requirements of various applications. Initially, the study utilizes chaos synchronization theory and the Routh–Hurwitz stability criterion to devise a feedback controller with a single input. This controller plays a crucial role in establishing a synchronization system specifically designed for memristive chaos. Subsequently, the FPGA design approach utilizing DSP Builder is employed to create models for both the single-input feedback controller and the memristive chaotic synchronization control system. This approach facilitates the efficient translation of these theoretical concepts into practical digital circuit implementations. Finally, the paper concludes with an experimental analysis that verifies the feasibility and practical applicability of the FPGA circuit design for memristive chaotic synchronization control.

Chaos synchronization of VCSELs with common injection of polarization-random light.

We propose and numerically demonstrate chaos synchronization of two vertical-cavity surface-emitting lasers (VCSELs) induced by common injection of constant-amplitude random-polarization light for physical key distribution. Results show that synchronization is sensitive to polarization rotation of injection light, and synchronization coefficients larger than 0.9 can be achieved as the rotation-degree mismatch is smaller than ±10°. Therefore, polarization rotation degree can serve as a hardware key parameter. Furthermore, each laser's output has no correlation to the constant amplitude of the injected light. Their components with identical polarization state, e.g. x or y polarization of VCSEL, also have low correlation coefficient smaller than 0.2. It is therefore believed that this synchronization scheme can provide a security-enhanced method of physical key distribution.

Secure WDM communication based on second order differential feedback electro-optical chaotic mutual injection synchronization

An optical phase chaos and mutual injection chaos synchronization scheme based on second order differential feedback electro-optical loop is proposed for chaotic communication. The filtered chaotic waves for mutual injection synchronization and multi-channel signals are transmitted through wavelength division multiplexing (WDM) to realize large-capacity confidential communication. The results show that the bandwidth of the optical chaos is 41.38 GHz, the normalized permutation entropy is 0.999, and the chaos has the performance of time delay suppressing (TDS). This scheme achieves up to 7-channel 25 GBaud 16QAM with the multi-modulus algorithm (MMA) algorithm at OSNR of 25 dB after 100 km transmission. The bit-rate distance of 280,000 Gb/s km is successfully realized by 500 km transmission of 4-channel 35 GBaud 16QAM signals at 25 dB OSNR. The analysis proves that the performance of the second order digital differential electro-optical phase feedback (2nd order DEOP) chaos is better than that of the 1st order DEOP chaos and 3rd order DEOP chaos. The 2nd order DEOP chaos can be generated at a smaller feedback coefficient, the bandwidth of radio frequency chaos is wider, and the TDS suppression is better. This scheme realizes high-speed and large-capacity secure optical chaos communication, which can be widely used in WDM networks and has practical feasibility and application value.

Coupling Dependence on Chaos Synchronization Process in a Network of Rulkov Neurons

This paper investigates the impact of network conformation on chaos synchronization in driven complex networks in a master-slave setting. We analyze the control and prediction of complex networks under perturbations. Although chaotic dynamics suppression is well understood in low-dimensional systems, it is not well described in more complex ones. To assess a network’s ability to amplify or suppress disturbances, we track ensembles of possible trajectories in the driven subsystem which give insights into nonlocal convergence properties in a master-slave setting. We demonstrate how the stability of forced networks of Rulkov neurons is dependent on network coupling architecture and how the duration of chaotic transients depends on initial conditions. Furthermore, we find that each network generator algorithm has specific sets of parameters that can lead to stable or nonstable states. Our results indicate that network types are more critical than isolated connections for suppressing chaotic dynamics in driven networks. Finally, we identify that under certain circumstances, the transient period before synchronization correlates with high convergence rates for certain initial conditions. This suggests nonuniform convergence rates in the phase space of driven neural networks.

Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control

In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems.

Chaos Synchronization of InGaAsP Lasers

The optical output of a semiconductor laser can fluctuate chaotically by modulating its direct current in limited conditions of the modulated current signal parameters in terms of modulation frequency and modulation index. In this work, single, double, and chaotic pulses of an InGaAsP laser with direct current modulation, are numerically presented through a bifurcation diagram. Numerically, the unidirectional optical coupling system realizes chaotic synchronization between two identical InGaAsP lasers with direct current modulation, as the transmitter/receiver configuration. The transmission time for transmitting light from the transmitted laser to the received laser is essential for controlling the quality of chaos synchronization. The transmission time applies on the order of nanoseconds. Chaos synchronization quality is estimated by a correlation plot and calculated by the cross-correlation coefficient. This study observed the best synchronization quality (complete chaos synchronization) when the two lasers are identical. On the other hand, the chaotic synchronization between two non-identical InGaAsP lasers was investigated. In this case, complete chaos synchronization is not found, and the quality of chaotic synchronization was observed to decrease as the mismatch between the parameters of the two lasers increased.

Adomian Decomposition, Firing Change Process Analysis and Synchronous Control of Fractional-Order Hindmarsh–Rose Neurons in Electromagnetic Field

In this paper, based on integer-order Hindmarsh–Rose (HR) neurons under an electric field, the fractional-order model is constructed, and the nonlinear term is decomposed by the Adomian decomposition method, and the numerical solution of the system is obtained. The firing behavior of the neuron model is analyzed by using a phase diagram, interspike interval (ISI) bifurcation diagram, sample entropy (SE) complexity, and largest Lyapunov exponent (LLE). Based on the sliding mode control theory, a chaos synchronization controller of the system is designed. Matlab simulation results show that the controller is realizable and effective, and also has the characteristic of fast response, which provides a reference for the control and application of a memristor neural network system.

Revealing Chaos Synchronization Below the Threshold in Coupled Mackey–Glass Systems

This study presents a novel concept in chaos synchronization, delta synchronization of chaos, which reveals the presence of chaotic models evolving in unison even in the absence of generalized synchronization. Building upon an analysis of unpredictability in Poincaré chaos, we apply this approach to unilaterally coupled time-delay Mackey–Glass models. The main novelty of our investigation lies in unveiling the synchronization phenomenon for a coupling constant below the synchronization threshold, an unattainable domain for conservative methods. Furthermore, we rigorously examine the coexistence of generalized synchronization and complete synchronization of unpredictability, which is a special case of delta synchronization, above the threshold. Therefore, the threshold is no longer a requirement for the synchronization of chaos in view of the present results. Additionally, transitions to fully chaotic regimes are demonstrated via return maps, phase portraits, and a bifurcation diagram. The findings are substantiated by tables and novel numerical characteristics.

A deep reinforcement learning method to control chaos synchronization between two identical chaotic systems

We propose a model-free deep reinforcement learning method for controlling the synchronization between two identical chaotic systems, one target and one reference. By interacting with the target and the reference, the agent continuously optimizes its strategy of applying perturbations to the target to synchronize the trajectory of the target with the reference. This method is different from previous chaos synchronization methods. It requires no prior knowledge of the chaotic systems. We apply the deep reinforcement learning method to several typical chaotic systems (Lorenz system, Rössler system, Chua circuit and Logistic map) and its efficiency of controlling synchronization between the target and the reference is demonstrated. Especially, we find that a single learned agent can be used to control the chaos synchronization for different chaotic systems. We also find that the method works well in controlling chaos synchronization even when only incomplete information of the state variables of the target and the reference can be obtained.

An Image Recognition Method Based on Dynamic System Synchronization

Abstract: At present, image recognition technology first classifies images and outputs category information through the neural network. The next step involves the search. Before retrieval, the feature database needs to be established, followed by one-to-one correspondence. This method is tedious, time-consuming and has low accuracy. In computer vision research, researchers have proposed various image recognition methods to be applied in various fields and made many research achievements. However, at present, the accuracy, stability and time efficiency cannot meet the needs of practical work. In terms of UAV image recognition, high accuracy and low consumption are required. Previous methods require huge databases, which increases the consumption of UAVs. Taking aerial transmission and line images as the research object, this paper proposes a method of image recognition based on chaotic synchronization. Firstly, the image is used as a function to construct a dynamic system, and the function structure and parameters are adjusted to realize chaos synchronization. In this process, different types of images are identified. At the same time, we research this dynamic system characteristics and realize the mechanism of image recognition. Compared with other methods, the self-built aerial image data set for bird's nest identification, iron frame identification and insulator identification has the characteristics of a high identification rate and less calculation time. It is preliminarily proven that the method of synchronous image recognition is practical, and also worthy of further research, verification and analysis.

Nonlinear quantum dot light emitting diode dynamics and synchronization with optoelectronic feedback

We studies a three-variable dimensionless model for a quantum dot light emitting diode (QD-LED) subject to optoelectronic feedback (OEFB). In dependence of the feedback strength and delay-time we analyze complex bifurcation scenarios for the intensity of the emitted light as well as time series, fast Fourier translate (FFT) and phase plane of all dynamic variables in order to elucidate the dynamics of the light emitting diode. The chaotic dynamic is completely determined by both the variation of the OEFB strength and delay-time of the QD-LED, as evidenced by bifurcation diagram. Our results show that small delay time lead to repeat periodicity of the light emitting towards OEFB. Furthermore, we study chaos synchronization of two QD-LED which are coupled via a unidirectional and bidirectional coupling system. When periodic systems are non-identical, both unidirectional and bidirectional systems depending on the coupling strength parameter the system exhibits completely synchronization. Residual chaos, the mean coherence and entropy are discussed as well.

Wideband chaos synchronization using discrete-mode semiconductor lasers.

Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.

Chaos synchronization for a class of uncertain chaotic supply chain and its control by ANFIS

In this paper, modelling of a three-level chaotic supply chain network. This model has the uncertainty of the retailer in the manufacturer. An adaptive neural fuzzy method has been proposed to synchronize the two chaotic supply chain networks. To train adaptive neural fuzzy controller, first, a nonlinear feedback control method is designed. Then, using Lyapanov theory, it is proved that the nonlinear feedback controller can reduce the synchronization error to zero in a finite time. The simulation results show that the proposed neural fuzzy controller architecture well controls the synchronization of the two chaotic supply chain networks. In the other part of the simulation, a comparison is made between the performance of the nonlinear controller and the adaptive neural fuzzy. Also, in the simulation results, the controller signal is depicted. This signal indicates that the cost of implementation in the real world is not high and is easily implemented.