Attractor and Invariance of a Class of Chaotic Dynamic Systems

2013 ◽  
Vol 787 ◽  
pp. 1093-1096
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Dynamic Systems ◽  
Chaotic Dynamic ◽  
Invariant Set ◽  
Positive Invariant Set

Chaos has been found to be very useful and has great potential in information and computer sciences and so on. In the paper a class of chaotic dynamic systems is studied. Moreover, the globally exponentially attractive set and positive invariant set of the chaos systems are given under some conditions. Finally an example is given to illustrate the result.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

GLOBALLY EXPONENTIALLY ATTRACTIVE SETS AND POSITIVE INVARIANT SETS OF THREE-DIMENSIONAL AUTONOMOUS SYSTEMS WITH ONLY CROSS-PRODUCT NONLINEARITIES

2013 ◽  
Vol 23 (01) ◽  
pp. 1350007 ◽  
Author(s):  
XINQUAN ZHAO ◽  
FENG JIANG ◽  
JUNHAO HU
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Cross Product ◽  
Invariant Set ◽  
Invariant Sets ◽  
Special Cases ◽  
Attractive Sets ◽  
Positive Invariant Set

In this paper, the existence of globally exponentially attractive sets and positive invariant sets of three-dimensional autonomous systems with only cross-product nonlinearities are considered. Sufficient conditions, which guarantee the existence of globally exponentially attractive set and positive invariant set of the system, are obtained. The results of this paper comprise some existing relative results as in special cases. The approach presented in this paper can be applied to study other chaotic systems.

ON FEEDBACK CONTROL OF CHAOTIC NONLINEAR DYNAMIC SYSTEMS

1992 ◽  
Vol 02 (02) ◽  
pp. 407-411 ◽  
Author(s):  
GUANRONG CHEN ◽  
XIAONING DONG
Keyword(s):  
Feedback Control ◽  
Computer Simulations ◽  
Discrete Time ◽  
Dynamic Systems ◽  
Chaotic Dynamic ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Nonlinear Dynamic Systems ◽  
Feedback Controls ◽  
Feedback Controllers

In this paper, some interesting analysis and simulations on the control of chaotic dynamic systems using conventional feedback control strategies are presented. The typical discrete-time chaotic Lozi system is investigated in some detail. The trajectories of the chaotic Lozi system are controlled to its equilibrium points using conventional feedback controls. Analysis on the design of the feedback controllers and its computer simulations are included.

Multiobjective analysis of chaotic dynamic systems with sparse learning machines

2006 ◽  
Vol 29 (1) ◽  
pp. 72-88 ◽  
Author(s):  
Abedalrazq F. Khalil ◽  
Mac McKee ◽  
Mariush Kemblowski ◽  
Tirusew Asefa ◽  
Luis Bastidas
Keyword(s):  
Dynamic Systems ◽  
Chaotic Dynamic ◽  
Sparse Learning ◽  
Learning Machines ◽  
Multiobjective Analysis
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