新的分数阶混沌系统及其同步控制

研究了一个新的分数阶系统的混沌动力学行为.基于分数阶微积分理论和数值模拟,发现在该新的分数阶系统中存在混沌,并且得出该分数阶系统能产生混沌吸引子的最低阶数为2.49阶.根据分数阶动力系统稳定性理论,通过设计非线性控制器,实现了新的分数阶混沌系统的投影同步,该方法设计简便,并且不需要计算Lyapunov指数,数值模拟结果验证了该同步方法的有效性.     

A simple fractional-order chaotic system without equilibrium and its synchronization

There has been an increasing interest in discovering no-equilibrium chaotic systems recently. In this paper, a novel three dimensional fractional-order chaotic system, which has no equilibrium, is introduced. Dynamics of the system has been studied. It is interesting that the system can exhibit coexisting chaotic attractors for the order as low as 2.7. The adjustable feature of a variable is studied by introducing a single controlled constant. Circuit implementation of the system is proposed to show its feasibility. In addition, we have designed the controllers to investigate coexisting synchronization types of such a new fractional-order system. Numerical examples have verified the proposed synchronization schemes.     

Coexistence of infinite attractors in a fractional-order chaotic system with two nonlinear functions and its DSP implementation

In this paper, a new five-dimensional fractional-order chaotic system based on two nonlinear functions is constructed. The rich dynamical behaviors of the system are analyzed by phase diagram, bifurcation diagram and Lyapunov exponents spectrum. In addition, the complexity of the fractional-order system is analyzed through Spectral Entropy (SE) and Permutation Entropy (PE) algorithms. Meanwhile the phenomenon of coexisting infinite attractors is analyzed. Of particular concern is that the phenomenon of multi-state transition and intermittent oscillation chaos is found in this new chaotic system. Furthermore, the system is implemented on the DSP platform. To the best of the knowledge, these rich dynamical characteristics and complicated phenomena are of great reference value in chaotic image encryption and other fields.     

忆阻开关混沌电路及其吸引子共存现象研究

为了研究忆阻开关电路的动力学行为,该文提出一种具有多吸引子共存现象的忆阻开关混沌电路。在该电路中存在多吸引子分岔,当系统中发生边界碰撞之后,系统中将产生不同的吸引子共存现象。其中包括单周期极限环与混沌吸引子共存,不同的混沌吸引子共存,对称的2周期极限环共存现象,以及对称的2周期极限环与5周期极限环共存现象等。该文通过相图、分岔图等数值仿真,分析了该电路的动力学行为,并利用PSIM电路仿真验证了其电路的可行性,对开关电路中多吸引子共存现象和混沌应用的研究具有重要意义。     

Complete and generalized chaotic synchronization in a system of three interacting maps

The bifurcation decay of complete chaos synchronization and the mechanisms of transition to partial synchronization of regular and chaotic oscillations are considered in a ring of three logistic maps with symmetric diffusion coupling. The modes of partial chaos synchronization are shown to be at the same time the modes of generalized chaotic synchronization.     

Chaos generation in fractional-order switched systems and its digital implementation

A double-scroll chaotic attractor generated by a fractional-order switched system is presented. Based on unstable dissipative systems (UDS) and a switching law, a fractional-order UDS is proposed. Chaos behavior is found with a fractional order as low as 2.568 by satisfying the stability criterion for fractional order chaotic systems. The fractional-order switched system is transformed to an equivalent switched system with augmented states. Then, the equivalent system is straightforward implemented on an ARM system-on-chip board by using Python high level programming language. Numerical simulations are in good agreement with experimental results, which demonstrates the usefulness of proposed method. Additionally, the test 0–1 and a chaos definition for finite state sets are given to demonstrate chaotic behavior. Finally, a random number generator is also proposed as a possible application.     

Electronic simulation and microcontroller real implementation of an autonomous chaotic and hyperchaotic system made of a Colpitts-Josephson junction like circuit

Most of the simple Josephson junction (JJ) based circuits with chaotic behavior found in the literature are nonautonomous. Hyperchaotic JJ-based circuits are often either driven by an external force or result from coupling chaotic circuits. An autonomous simple circuit based on Josephson junction active element (JJ), with exactly three physical energy storage tanks, is proposed and analyzed in this paper. This Colpitts-like CLC circuit, though operating at low frequencies, can generate hyperchaotic signals when its nonlinear element is a resistive–capacitive–inductance shunted junction (LRCLSJ) model. Two equilibrium points are found, and their stability analysis is investigated. The proposed circuit displays Hopf bifurcation, periodic oscillations, chaotic and hyperchaotic attractors. The electronic implementation of the proposed circuit using OrCAD-PSpice software is presented to confront the numerical simulations results. A good qualitative agreement is revealed by comparing the analog and numerical simulations results. At last, the microcontroller real implementation is presented using Arduino UNO board. The results obtained are in good agreement with the numerical simulation results.

     

Inducing Chaos in Electronic Circuits by Resonant Perturbations

We propose a scheme to induce chaotic attractors in electronic circuits. The applications that we are interested in stipulate the following three constraints: 1) the circuit operates in a stable periodic regime far away from chaotic behavior; 2) no parameters or state variables of the circuit are directly accessible to adjustment and 3) the circuit equations are unknown and the only available information is a time series (or a signal) measured from the circuit. Under these conditions, a viable approach to chaos induction is to use external excitations such as a microwave signal, assuming that a proper coupling mechanism exists which allows the circuit to be perturbed by the excitation. The question we address in this paper is how to choose the waveform of the excitation to ensure that sustained chaos (chaotic attractor) can be generated in the circuit. We show that weak resonant perturbations with time-varying frequency and phase are generally able to drive the circuit into a hierarchy of nonlinear resonant states and eventually into chaos. We develop a theory to explain this phenomenon, provide numerical support, and demonstrate the feasibility of the method by laboratory experiments. In particular, our experimental system consists of a Duffing-type of nonlinear electronic oscillator driven by a phase-locked loop (PLL) circuit. The PLL can track the frequency and phase evolution of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors     

Theoretical model of optical fiber secure communication system with chaotic multiple-quantum-well lasers

Chaotic synchronization of injected multiple-quantum-well lasers of optical fiber system and a theoretical model of optical fiber chaotic secure communication system are presented by coupling a chaotic multiple-quantum-well laser synchroniza- tion system and a fiber channel. A new chaotic encoding method of chaos phase shift keying On/Off is proposed for optical fiber secure communications. Chaotic synchronization is achieved numerically in long-haul fiber system at wavelength 1.55 μm. The effect of the nonlinear-phase of fiber is analyzed on chaotic signal and synchronization. A sinusoidal signal of 0.2 GHz frequency is simulated numerically with chaos masking in long-haul fiber analog communication at wavelength 1.55 μm while a digital signal of 0.5 Gbit/s bit rate is simulated numerically with c1haos masking and a rate of 0.05 Gbit/s are also simulated numerically with chaos shift keying and chaos phase shift keying On/Off in long-haul fiber digital communica- tions at wavelength 1.55 μm     

Multistability and synchronization of chaos in maps with “Internal” coupling

Bifurcation mechanisms responsible for the loss of the complete synchronization of chaos and for formation of multistability in a system with a unidirectional “internal” coupling are considered. The sequence of stages during which chaotic synchronization decays is described. A quantitative analysis of chaotic synchronization is performed.     

A New Fractional-Order Chaotic System and Its Synchronization with Circuit Simulation

A new fractional-order chaotic system is proposed in this paper, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, a circuit diagram is studied to realize the fractional-order chaotic system. The new fractional-order chaotic system can be controlled to reach synchronization based on the nonlinear control theory, and the results between numerical emulation and circuit simulation are in agreement with each other.     

基于主动-被动法对电光双稳态系统的混沌控制和同步研究

将主动-被动同步法改进后,用于对长延迟状态下电光双稳态系统进行混沌控制和同步研究,分别采用单向驱动方法和驱动-耦合方法研究电光双稳态系统的混沌控制和同步。数值模拟表明,在适当参数条件下应用单向驱动方法,驱动系统可以将响应系统控制到各周期状态,且驱动系统的状态决定了响应系统的状态;适当选取耦合系数和驱动强度,两种方案都可以实现驱动系统与响应系统之间的混沌同步。从同步效果上来看,驱动-耦合方法所需耦合系数更小,可控的耦合系数范围比较广,同步效果更好。     

Complex dynamics of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight: Coexistence of multiple attractors and remerging Feigenbaum trees

This contribution investigates the nonlinear dynamics of a model of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight. The investigations show that the proposed HNNs model possesses three equilibrium points (the origin and two nonzero equilibrium points) which are always unstable for the set of synaptic weights matrix used to analyze the equilibria stability. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents graph, phase portraits and frequency spectra, are used to highlight the rich and complex phenomena exhibited by the model. These rich nonlinear dynamic behaviors include period doubling bifurcation, chaos, periodic window, antimonotonicity (i.e. concurrent creation and annihilation of periodic orbits) and coexistence of asymmetric self-excited attractors (e.g. coexistence of two and three disconnected periodic and chaotic attractors). Finally, PSpice simulations are used to confirm the results of the theoretical analysis.     

一种新型双忆阻混沌系统动力学及其电路实现研究

在经典的蔡氏混沌电路基础上,引入三次非线性磁控忆阻模型,利用一个磁控忆阻模型和一个荷控忆阻模型,外加一个负电导替换变形蔡氏电路中的蔡氏二极管,设计了一个五阶混沌电路,用常规的方法研究系统的基本动力学特性。通过数值仿真结果表明电路在参数变化情况下能产生Hopf分岔和反倍周期分岔两种分岔行为,并能产生双涡卷、单涡卷、极限环、同宿轨等不同轨道,出现了双单摆运动。观察混沌吸引子推广到功率与能量信号,观察到蝴蝶翅膀重叠的奇异吸引子。通过改变初始值,能产生共存吸引子和周期极限环共存现象。为了验证电路的混沌行为,将对设计的电路进行了PSpice仿真,电路仿真结果验证了理论分析的正确性。     

含无损传输线的约瑟夫森结电磁系统中的分岔与混沌

 建立了含无损传输线的约瑟夫森结电磁系统左端点处电压正向行波分量的一维Poincaré映射模型,运用非线性动力学理论分析了映射定点的稳定性。通过数值计算得到了映射随电压反射系数变化的分岔图,详细分析了系统随参数变化的动态演化过程。结果表明在一定参数条件下,该电磁系统中存在着分岔、混沌、周期吸引子共存、混沌吸引子共存以及周期与混沌吸引子共存等复杂的非线性动力学行为。     

A Novel Secure Data Transmission Scheme in Industrial Internet of Things

The industrial Internet of Things(IoT)is a trend of factory development and a basic condition of intelligent factory.It is very important to ensure the security of data transmission in industrial IoT.Applying a new chaotic secure communication scheme to address the security problem of data transmission is the main contribution of this paper.The scheme is proposed and studied based on the synchronization of different-structure fractional-order chaotic systems with different order.The Lyapunov stability theory is used to prove the synchronization between the fractional-order drive system and the response system.The encryption and decryption process of the main data signals is implemented by using the n-shift encryption principle.We calculate and analyze the key space of the scheme.Numerical simulations are introduced to show the effectiveness of theoretical approach we proposed.     

Chaos in the Fractional Order Logistic Delay System

In this paper, we study the chaotic behaviors in a fractional order logistic delay system. We find that chaos exists in the fractional order logistic delay system with an order being less than 1. In addition, we numerically simulate the continuances of the chaotic behaviors in the logistic delay system with orders from 0.1 to 0.9. The lowest order we find to have chaos in this system is 0.1. Then we further investigate two methods in controlling the fractional order chaotic logistic delay system based on feedback. Finally, we investigate a lag synchronization scheme in this system. Numerical simulations show the effectiveness and feasibility of our approach.     

分数阶忆阻退化Jerk系统的特性分析与DSP实现

为了探究分数阶形式下该类系统的动力学特性,该文将分数阶微积分引入到忆阻退化Jerk系统中,增加了一个自由度,提升了系统性能。通过相图、分岔图、李雅普诺夫指数谱、复杂度混沌图等分析了系统的动力学特性,并采用DSP技术,实现了该系统的数字电路。研究结果表明,系统拓展到分数阶后有两种不同的单涡卷吸引子,系统随初值变化呈现倍周期分岔路径,在某些特定初值处系统演化路径出现跃变。系统具有无限多个吸引子共存。     

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics,Hardware implementation and Image encryption application

In this paper, a new method for generating multi-scroll chaotic attractors via constructing a compound hyperbolic tangent-cubic nonlinear function in canonical Chua’s circuit is presented. The basic dynamic characteristics of the system are analyzed, including equilibrium points, bifurcation diagrams, Lyapunov exponents, phase portraits, time-domain diagrams and attractive basins. What is surprising is that the proposed multi-scroll Chua’s circuit also exhibits rich dynamic behaviors like coexisting multiple attractors, transient period, intermittent chaos and offset boosting. In addition, we put forward the application of the system in chaotic image encryption, and analyzed some security performance evaluation indexes to show that the new Chua’s chaotic cipher system has high security and reliable encryption performance. Finally, the hardware design and experiments of the chaotic digital circuits and image encryption are carried out. Both numerical simulation and FPGA experimental results verify the feasibility and usability of the proposed new multi-scroll Chua’s system.     

两台非全同激光器的混沌同步

对空间上相互耦合的两台非全同固体激光器的动力学行为进行了分析。当两台激光器的抽运受到调制而每台激光器的损失不同时 ,两台激光器输出的强度会出现周期性运动、混沌同步和失去同步的情况。激光中混沌同步的发生 ,同两台激光器之间的耦合程度有关。当耦合较强时发生周期性运动 ,耦合适中时处于混沌状态 ,在特定条件下产生混沌同步 ,而耦合较小时 ,两台激光器的振荡就相对独立。