准对称流的混沌和共振流线

采用计算Melnikov函数的方法 ,研究了描述qth(q=3或 6 )准对称流流体粒子运动的动力系统 .文中在分析未扰动系统轨道解析表示的基础上 ,深入考察了扰动系统的分岔情况 .结果表明 ,扰动系统在一定条件下能够分支出混沌和共振流线 .     

关于周期吸附系统的分布混沌的注记

设X是一个紧致度量空间,f X→X是一个连续映射.若存在f的一个m-周期点p和另一个m'-周期点q(p≠q),使得对任意非空开集V(C)X,都有{p,q}(C)∞ Un=0fn(V),则称动力系统(X,f)是一个(m,m')型周期吸附系统.证明了:1)若(X,f)是一个(m,m')型周期吸附系统且X是自密的,则对任一给定的正整数k,存在一个fk的的分布混沌集S,使得S与X的任一非空开集之交均含有一个Cantor集;2)若(X,f)是一个(m,m')型周期吸附系统且拓扑共轭于(X ',f'),则(X ',f')也是一个(m,m')型周期吸附系统.改进和推广了已有结果.     

Special dynamic behaviors of a temporal chaotic system

When dynamic behaviors of temporal chaotic system are analyzed,we find that a temporal chaotic system has not only genetic dynamic behaviors of chaotic reflection,but also has phenomena influencing two chaotic attractors by original values.Along with the system parameters changing to certain value,the system will appear a break in chaotic region,and jump to another orbit of attractors.When it is opposite that the system parameters change direction,the temporal chaotic system appears complicated chaotic behaviors.     

Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems

This work presents a direct approach to design stabilizing controller based on a special matrix structure to synchronize chaotic systems and extends the approach to synchronize fractional chaotic systems. With this method, chaos synchronization is implemented in Lorenz chaotic systems with known parameters and the same to Lorenz chaotic systems with unknown parameters. Especially, fractional Lorenz chaotic system with unknown parameters is synchronized by fractional Chen chaotic system too. Numerical simulations confirm the effectiveness of the method proposed.     

Adaptive synchronization to a general non-autonomous chaotic system and its applications

In this paper, new adaptive synchronous criteria for a general class of n-dimensional non-autonomous chaotic systems with linear and nonlinear feedback controllers are derived. By suitable separation between linear and nonlinear terms of the chaotic system, the phenomenon of stable chaotic synchronization can be achieved using an appropriate adaptive controller of feedback signals. This method can also be generalized to a form for chaotic synchronization or hyper-chaotic synchronization. Based on stability theory on non-autonomous chaotic systems, some simple yet less conservative criteria for global asymptotic synchronization of the autonomous and non-autonomous chaotic systems are derived analytically. Furthermore, the results are applied to some typical chaotic systems such as the Duffing oscillators and the unified chaotic systems, and the numerical simulations are given to verify and also visualize the theoretical results.     

一种改进的混沌序列产生方法

根据灰度图像的二维直方图的特点,在已有的二维Arnold混沌系统的基础上,结合Bernstein形式的Bézier曲线的生成算法,给出了一种基于生成Bézier曲线的de Casteljau算法构造伪随机序列的方法,实验结果表明生成的二维序列不仅具有伪随机性,而且还具有在近似圆盘中随机分布的性质,这使得该伪随机序列更适合对灰度图像的二维灰度直方图进行基于混沌优化的图像分割.在此基础上,给出了一种基于混沌优化的二维最大熵的灰度图像分割算法,该算法对于含噪图像取得了良好的分割效果.     

A new chaotic cryptosystem

Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned.     

On chaotic graphs and applications in physics and biology

El Naschie’s ε^∞ theory in Quantum space time is given and discussed geometrically and topologically as a category of fuzzy spaces, these fuzzy categories in which lines are fuzzy fractal lines. In this paper, we represent the chaotic graphs as many fuzzy fractal lines up to ∞. We will describe them by chaotic matrices. Many fuzzy systems (chaotic systems) are described and applied in [8], [9], [10], [11], [12]. This article introduces some operations on the chaotic graphs such as the union and the intersection; also both of the chaotic incidence matrices and the chaotic adjacency matrices representing the chaotic graphs induced from these operations will be studied. Theorems governing these studies are obtained. Some applications on chaotic graphs are given [18], [19], [20], [21].     

一类非线性混沌系统混沌吸引子的冲击控制

在国内外研究工作的基础上,给出了一类非线性混沌系统混沌吸引子的冲击控制方案,运用普适方程的冲击控制理论导出了这类混沌系统混沌吸引子的冲击控制渐进稳定的条件,利用这一条件给出了混沌吸引子渐进稳定冲击控制的区间上界,最后给出了许多数据结果,这些结果对于混沌吸引子的控制将有重要的参考价值．     

Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization

Chaos optimization algorithms (COAs) usually utilize the chaotic map like Logistic map to generate the pseudo-random numbers mapped as the design variables for global optimization. Many existing researches indicated that COA can more easily escape from the local minima than classical stochastic optimization algorithms. This paper reveals the inherent mechanism of high efficiency and superior performance of COA, from a new perspective of both the probability distribution property and search speed of chaotic sequences generated by different chaotic maps. The statistical property and search speed of chaotic sequences are represented by the probability density function (PDF) and the Lyapunov exponent, respectively. Meanwhile, the computational performances of hybrid chaos-BFGS algorithms based on eight one-dimensional chaotic maps with different PDF and Lyapunov exponents are compared, in which BFGS is a quasi-Newton method for local optimization. Moreover, several multimodal benchmark examples illustrate that, the probability distribution property and search speed of chaotic sequences from different chaotic maps significantly affect the global searching capability and optimization efficiency of COA. To achieve the high efficiency of COA, it is recommended to adopt the appropriate chaotic map generating the desired chaotic sequences with uniform or nearly uniform probability distribution and large Lyapunov exponent.     

Design of $n$-dimensional multi-scroll Jerk chaotic system and its performances

Based on three-order Jerk and high-order Jerk chaotic systems, a general approach is proposed to generate $n$-dimensional multi-scroll Jerk chaotic attractors via nonlinear control. Dynamics of the $n$-dimensional multi-scroll Jerk chaotic systems are analyzed by means of the largest Lyapunov exponent and multi-scale permutation entropy complexity. As an experimental verification, four-dimensional Jerk chaotic attractors are implemented by analog circuits. Results of the numerical simulation are consistent with that of the hardware experiments. It shows that the method of obtaining complex Jerk chaotic attractors is effective.     

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.     

SPECIAL DYNAMIC BEHAVIORS OF A TEMPORAL CHAOTIC SYSTEM

When dynamic behaviors of temporal chaotic system are analyzed, we find that a temporal chaotic system has not only generic dynamic behaviors of chaotic reflection, but also has phenomena influencing two chaotic attractors by original values. Along with the system parameters changing to certain value, the system will appear a break in chaotic region, and jump to another orbit of attractors. When it is opposite that the system parameters change direction, the temporal chaotic system appears complicated chaotic behaviors.     

Coexisting chaotic attractors in a single neuron model with adapting feedback synapse

In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra.     

Parameters identification of chaotic system by chaotic gravitational search algorithm

In this paper, for the parameter identification problem of chaotic system, a chaotic gravitational search algorithm (CGSA) is proposed. At first, an iterative chaotic map with infinite collapses is introduced and chaotic local search (CLS) is designed, then CLS and basic gravitational search are combined in the procedure frame. The CGSA is composed of coarse gravitational search and fine chaotic local search, while chaotic search seeks the optimal solution further, based on the current best solution found by the coarse gravitational search. In order to show the effectiveness of CGSA, both offline and online parameter identifications of Lorenz system are conducted in comparative experiments, while the performances of CGSA are compared with GA, PSO and GSA. The results demonstrate the effectiveness and efficiency of CGSA in solving the problem of parameter identification of chaotic system, and the improvement to GSA has been verified.     

Implementation of chaotic secure communication systems based on OPA circuits

In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible.     

低维混沌时序非线性动力系统的预测方法及其应用研究

主要研究由低维混沌时序所确定的非线性动力系统的预测方法及其应用。在国外学者研究工作的基础上,应用一种非线性混沌模型在相空间内对时序进行重构工作,先通过改进的最小二乘方法来估计模型的参数,满足一定精度后,再采用最优化方法来估计模型的参数,并用所求得的混沌时序模型在其相空间内对时序的未来值进行预测。给出了非常有代表性的实例对文中模型和算法进行验证。结果发现采用该算法能较准确地求得模型的参数,在相空间中对混沌时序进行预测,将传统方法中的外推变成了相空间中的内插,及选取最佳的模型阶数等工作都能增加预测的准确程度,且混沌时序不可能进行长期的预测。     

Counteracting the dynamical degradation of digital chaos via hybrid control

Chaotic systems would degrade owing to finite computing precisions, and such degradation often seriously affects the performance of digital chaos-based applications. In this paper, a chaotification method is proposed to solve the dynamical degradation of digital chaotic systems based on a hybrid structure, where a continuous chaotic system is applied to control the digital chaotic system, and a unidirectional coupling controller that combines a linear external state control with a modular function is designed. Moreover, we proof rigorously that a class of digital chaotic systems can be driven to be chaotic in the sense that the system is sensitive to initial conditions. Different from the existing remedies, this method can recover the dynamical properties of system, and even make some properties better than those of the original chaotic system. Thus, this new approach can be applied to the fields of chaotic cryptography and secure communication.     

Double crises in two-parameter forced oscillators by generalized cell mapping digraph method

By means of generalized cell mapping digraph method, a crisis of sinusoidally forced oscillators is observed as a system parameter is varied. The crisis happens when a chaotic attractor collides with a regular saddle or a chaotic saddle, and is called a regular crisis or a chaotic crisis, respectively. By increasing a small constant bias in the forcing and considering both the system parameter and bias together as controls, a double crisis vertex in a two-parameter plane is determined, at which four curves of crises meet and four distinct crises coincide. The two patterns of such a double crisis vertex are investigated, namely, two regular boundary crises compounded with two chaotic interior crises and two chaotic boundary crises compounded with two chaotic interior crises.     

A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system

This paper introduces a new 3-D quadratic autonomous system, which can generate two coexisting single-wing chaotic attractors and a pair of diagonal double-wing chaotic attractors. More importantly, the system can generate a four-wing chaotic attractor with very complicated topological structures over a large range of parameters. Some basic dynamical behaviors and the compound structure of the new 3-D system are investigated. Detailed bifurcation analysis illustrates the evolution processes of the system among two coexisting sinks, two coexisting periodic orbits, two coexisting single-wing chaotic attractors, major and minor diagonal double-wing chaotic attractors, and a four-wing chaotic attractor. Poincaré-map analysis shows that the system has extremely rich dynamics. The physical existence of the four-wing chaotic attractor is verified by an electronic circuit. Finally, spectral analysis shows that the system has an extremely broad frequency bandwidth, which is very desirable for engineering applications such as secure communications.