Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

一种超混沌映射的单双参量自适应同步

利用参量自适应法实现了超混沌系统Kawakami映射的同步.通过严密的数学推导,给出了Kawakami映射在单参量自适应下实现同步的充分条件,并在双参量自适应控制下系统同样实现了同步.数值模拟结果显示,该映射输出具有类似于白噪声的宽谱特性,因此比较适合用于保密通信.     

Theoretical and experimental time series analysis of an inductorless Chua’s circuit

In this paper we have analyzed the time series obtained from an experimental realization of an inductorless version of Chua’s circuit. We have also compared the experimental results with the results emerging by analysis of the time series obtained by numerical simulations of the respective model equations. Lyapunov exponent spectra, the Kaplan-Yorke dimension and phase-space diagrams were used to show the similarities between theoretical and experimental results. We were able to identify the effects of the operational amplifier simulated inductor internal resistance on the Chua’s circuit dynamics. Decreasing internal resistance for decreasing current through the circuit was responsible for the observed bifurcation route.     

利用单模激光Lorenz系统实现混沌反控制

利用Lyapunov函数方法，对混沌反控制问题进行了研究.以单模激光Lorenz系统和描述心脏搏动的Bonhoeffer-Van der Pol系统为例，设计了一种控制器，成功地使Bonhoeffer-Van der Pol系统混沌化.给出了控制器的具体设计方案以及单模激光Lorenz系统与Bonhoeffer-Van der Pol系统状态之间误差系统的结构.仿真结果表明，在控制器的作用下，Bonhoeffer-Van der Pol系统所有状态变量严格地跟踪了单模激光Lorenz系统的混沌轨迹，对应的相空间中Bonhoeffer-Van der Pol系统的轨迹也由极限环转变为与单模激光Lorenz系统的轨迹完全相同的混沌吸引子，Bonhoeffer-Van der Pol系统严格地跟踪了单模激光Lorenz系统混沌的动态行为.     

Nonuniform stability properties and perturbing lyapunov functions

In this paper, without assuming the conditions everywhere, we study nonuniform stability properties of differential systems by employing the method of perturbing Lyapunov functions and splitting the given system suitably     

Anti-synchronization of Liu system and Lorenz system with known or unknown parameters

This work is concerned with anti-synchronization of Liu system and Lorenz system. Based on Lyapunov stability theory, different controllers are designed to anti-synchronize the two non-identical chaotic systems, active control is used when parameters are known, while the adaptive control law and the parameter update rule are derived via adaptive control when parameters are uncertain. Moreover, the convergence speeds of the scheme can be adjusted by changing the control coefficients. Finally, numerical simulations are also shown to verify the results.     

Sufficient conditions for the local controllability of systems with random parameters for an arbitrary number of system states

We obtain sufficient conditions for the existence of a nonanticipating control for linear systems with stationary random parameters. We consider the case of a bounded control and an arbitrary number of system states. We estimate the probability that the system is nonanticipatingly locally controllable on a fixed time interval. We formulate the main assertions in terms of Lyapunov functions, choosing the latter in the class of piecewise continuously differentiable functions.     

Stability in critical cases of a holonomic mechanical system with two degrees of freedom subject to impacts

Stability conditions for a holonomic impulsive mechanical system with two degrees of freedom in the critical case of one pair of complex-conjugate multipliers are established. An analog of the first Lyapunov exponent is calculated __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 105–117, June 2008.     

带Markov调制的随机微分延迟方程的稳定性

本文采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶指数稳定性,并对其几乎必然指数稳定性也进行了探讨.