Chaotic System Based On Impulsive Control And Its Circuit Implementation

Chaos is a special state of motion existing in nonlinear systems.It has attracted extensive attention of experts and scholars because of its rich dynamic characteristics.Research has shown that chaotic systems with time-delay tend to have higher complexity,which made chaotization of time-delayed systems become a hot issue in the field of nonlinear systems research.Due to the complexity of theoretical analysis and circuit implementation,the chaotization problem of time-delayed systems realized by impulsive control has not been fully studied.Based on the existing chaotic system theory,time-delayed system theory and impulsive control theory,this thesis studies the chaotization problem of time-delayed system based on impulsive control,and verifies the correctness of theoretical analysis by numerical simulation and simulation circuit.Specifically,the major research contents and innovation points of this thesis are as follows:1.The influence of impulsive control on chaotic characteristics of time-delayed systems is analyzed in detail.By designing the suitable impulsive controller,we can either realize chaotization of a non-chaotic time-delayed system or make a time-delayed chaotic system more complicated,which means by applying appropriate impulsive control,we can turn a time-delayed chaotic system with a single singular attractor into a double scroll time-delayed chaotic system with two singular attractors.Using the simulation results of MATLAB,the chaotic characteristics of the system are analyzed from phase diagram,time sequence diagram,sensitivity test diagram of initial value,power spectrum,the maximum Lyapunov exponent and so on.Also the validity of the theoretical results is verified.2.Based on the principle of circuit design and the approximation principle of impulsive function,two kinds of impulse simulation circuits are designed for the time-delayed chaotic system with fixed-time impulse,namely the impulse circuit based on square wave circuit and the impulse circuit based on RC oscillation circuit.And two different interception methods are adopted in the impulse circuit based on square wave circuit.By comparing the impulses generated by different circuits,the impulse circuit with better effect is selected and applied to the previously discussed time-delayed system to build a complete impulsive time-delayed chaotic circuit.The experimental results show that the operation results of the simulation circuit are consistent with the numerical simulation results,which verifies the correctness of the theoretical analysis and the validity and feasibility of the impulse circuit and time-delayed chaotic circuit.