基于自适应控制的八个混沌系统的多级组合同步

针对传统的混沌系统结构样式单一和系统变量少的问题,设计了一种混沌电路系统,该电路有较为复杂的动力学行为、较高的敏感性和较强的抗干扰性。随着电路参数的变化,结合自适应稳定性判据和混沌运动理论详细分析了该系统的不同动力学行为;此外,根据电路图搭建了相应的电路并利用示波器观察该电路的动力学行为,其行为与MATLAB的仿真结果相一致,进一步证明了电路的可行性和灵活性。在此基础上,重点提出并研究了基于本系统的多级组合同步,通过构造不同的控制器实现了八个系统之间的多级组合同步。仿真结果表明,该同步方案在收敛速度和精度上具有很好的效果。     

基于参数自适应方法的统一混沌系统的同步控制

采用参数自适应控制方法，根据Lyapunov稳定性原理，通过构造适当的控制函数和设计参数的自适应控制律，分别实现了系统在不同确定参数和相同不确定参数两种情况下的统一混沌系统的同步导出在这两种情况下的统一混沌系统能实现同步的充分条件.相同不确定参数情况下的同步系统控制器结构更简单、同步性能更优．数值仿真证明了该方法的有效性．     

多翼统一混沌系统的自适应同步及反同步

研究一种多翼统一混沌系统的同步及反同步问题,这种统一混沌系统将多种多翼混沌系统结合起来,通过调节系统参数可产生不同类型的混沌吸引子。分析多翼混沌系统中新发现的四维混沌系统的动力学特性,这种四维混沌系统可以产生一种形状似蝙蝠的吸引子。通过对系统的相图、李雅普诺夫指数谱和分岔图等动力学行为进行分析和数值仿真,验证了该系统具有丰富的混沌特性。通过Lyapunov稳定性理论和自适应控制方法,设计合适的非线性反馈控制器以及参数自适应率,实现该混沌系统的自适应同步。利用扩维的方法,实现不同维数的非同族混沌系统间的自适应反同步,在MATLAB中进行数值仿真,验证了所设计控制器和给出的参数自适应率的有效性和可行性。     

时滞扰动Lorenz系统及其同步电路实现

以Lorenz系统为模型,构造一个具有多个正的Lyapunov指数的四维时滞混沌系统,分析了其基本动力学行为,并利用滤波网络技术对新系统进行了可切换电路设计.然后,基于Lyapunov方法给出了两个相同高维时滞系统的耦合同步条件,根据所提出的同步方法设计了自同步控制电路.实验表明了该时滞系统具有丰富的动力学行为,所设计的同步控制电路结构简单,易于实现,能够通过调节部分元件参数获得较好的同步性能.     

不同阶混沌系统的函数延迟投影同步研究*

针对通信混沌系统中存在着时间延迟现象,研究了两个阶数不同的混沌系统之间的函数延迟投影同步问题,基于Lyapunov稳定性理论,通过主动控制同步方法和自适应控制同步方法,分别实现了参数已知和参数未知的超混沌Lü系统和混沌Liu系统间的函数延迟投影同步。最后通过仿真实验证明了所采用方法的可行性和有效性。     

一类新的时滞混沌系统及其最小能量引导控制

提出了一类时滞混沌系统.从最大Lyapunov指数、相图和分叉图3个方面,揭示这类系统随其参数变化所产生的丰富动力学行为,并发现了大幅度拟周期(弱混沌)振荡现象,分析了这种振荡在工业中的危害以及可能的用途.提出了异时滞的高维混沌系统间的同步控制问题,并提出一种基于变增益反馈的最小能量控制法,用线性反馈控制器实现了快速的引导控制.因为反馈增益由一个小量随着同步误差的减小逐渐增大,本文提出的控制器可以有效减小控制所需的能耗.     

参数自适应控制的混沌同步研究

在对同步系统特性分析的基础上,利用参数自适应控制混沌原理,提出了一种混沌系统在不同系统参数下的混沌同步方法.在参数自适应控制方程中,采用了分段控制与非线性反馈控制相结合的控制函数.通过选取合适的控制律和控制参数可以实现不同系统参数的两个 logistic映射的混沌同步.基于 Matlab软件的数值仿真的结果表明该方法是控制离散混沌系统同步化的一种快速有效的方法.     

Newton-Leipnik系统的多种吸引子及其形成机制

研究了Newton-Leipnik混沌系统的各种动力学行为,从中发现了新的双体双核混沌吸引子,发现了混沌吸引子与小周期吸引子、大周期吸引子并存于同一相空间的各种情况,发现了趋于周期吸引子的暂态混沌运动。这些特性是由五个平衡点的属性所确定的。每个平衡点邻域的状态轨线沿某方向发散而沿某方向收敛,这导致了系统复杂的动力学行为发生。     

分数阶异结构超混沌系统完全同步与反相同步控制

以分数阶Lü混沌系统和分数阶Chen超混沌系统为例,研究了维数不同、分数阶次不相等的异结构的混沌系统和超混沌系统的完全同步和反相同步.首先,基于分数阶系统稳定性理论和非线性动力学理论,构造出相应的非线性控制器,实现了两个维数不同,分数阶次不相等异结构混沌系统与超混沌系统的完全同步和反相同步;其次,基于分数阶稳定性理论,对上述两类同步给出了严格的数学证明;最后,借助于预估-校正算法,利用数值模拟验证了所提方法的有效性.     

两自由度齿轮传动系统全局动力学研究

齿侧间隙的存在,使齿轮传动系统存在着丰富的非线性动力学行为.考虑两自由度齿轮传动系统的动力学模型,利用数值方法分析系统的分岔和混沌动力学行为.通过简单胞映射方法对非线性齿轮系统进行全局分析,得到系统的吸引子,吸引域等全局特性.结果显示:随着激振频率的变化,系统存在多个周期解共存以及周期解与混沌运动共存现象.最后利用系统的相轨线图与庞加莱截面图进行对比分析,在不同的初值条件下,系统呈现出不同的周期运动或混沌运动.利用简单胞映射方法的数值计算结果可以实现在不良参数条件下,通过合理控制系统的初值条件而获得理想的系统响应.     

Chaos control and hybrid projective synchronization for a class of new chaotic systems

The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.     

Some synchronization criteria for bidirectionally-coupled chaotic systems

1IntroductionChaos synchronization,as a very important topic in thenonlinear science ,has been developed extensivelyinthelastfew years [1,2] .A wide variety of approaches [1 ~9]have been proposed for the synchronization of chaoticsystems which include linear and nonlinear feedback,adaptive control ,etc . Most of the methods mentionedabove synchronize two coupled identical chaotic systems .Accordingto the condition of coupling signal ,they can beclassified into bidirectional [3 ~5] and unidirec…     

Some synchronization criteria for bidirectionally-coupled chaotic systems

Based on the stability theory of linear time-varying continuous system,this paper investigates the synchronization of two linear bidirectionally-coupled systems.Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback.Since the trajectory of chaotic system is continuous and bounded,one can choose suitable coupled parameters to satisfy the proposed criterion.The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling.The chaotic Chen system and the generalized Lorenz-like system are taken as examples,the simulations verify the effectiveness of the proposed method.     

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.     

Some new criteria for lag synchronization of chaotic Lur＇e systems by replacing variables control

Some new criteria for the chaotic lag synchromzation are proposed. At first, lag synchronization scheme for identical master-slave Lur‘e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchromzation are described. Then. based on a quadratic Lyapunov function, two new Lur‘e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are apphed to analyze the lag synchromzation of general master-slave Chua‘s circuits so that some ranges of the parameters in which the master-slave Chua‘s circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.     

Rewiring-induced chaos in pulse-coupled neural networks

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node-like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.     

混沌系统与稳定系统的同步控制研究

通过对异结构混沌系统的广义投影同步进行分析研究,发现其本质为利用驱动系统的输出信号构造合适的非线性反馈控制器,使得响应系统具有和驱动系统相一致的拓扑结构,从而两系统可以同步.在此基础上,认为只要构造一个合适的控制器就有可能使得一个混沌系统和任意一个系统发生同步,数值仿真主要针对一个稳定系统,构造合适的非线性反馈控制器,实现其和一个四维混沌系统的广义投影同步,表明了理论推导的正确性和所设计的控制器的有效性.     

兴奋性化学突触耦合的神经元的同步

基于动力系统的稳定性理论、数值计算分岔图和线性化系统的最大Lyapunov指数,研究了经兴奋性化学耦合的快峰神经元的同步动力学.研究表明,随着一些关键参数的改变,耦合神经元能呈现丰富的同步行为,如各种周期的同步和混沌的同步.研究结果对理解神经元系统的同步运动具有指导意义.     

连续及采样异结构混沌同步控制

研究了一类异结构混沌全状态同步控制问题。分别以Coullet系统与Rossler系统为目标和响应系统,采用backstepping方法设计了保持两系统之间所有状态同步的连续时间控制器,为了把连续控制器更好地应用到计算机采样控制系统中,在连续控制器设计的基础之上,基于采样系统实用半局渐近稳定理论,又进行了采样同步控制器的再设计研究。仿真结果证明了所设计的连续及采样同步控制器的有效性,并进一步表明所设计的采样同步控制器,与由连续控制器直接离散化所得的控制器相比,具有更快的收敛速度,而且在保证系统稳定的前提下还具有更宽的采样周期选择范围。     

Converting chaos into periodic motion by state feedback control

A simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable. The low-periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics. Melnikov's perturbation method in generalized Hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low-periodic motion in the Lorenz equations. Moreover, the existence of periodic orbits is examined in the perturbed Lorenz system. Simulation results verify the effectiveness of Melnikov's analysis.