The Design Of Heterogeneous Fractional-order Chaotic System And Its Multiple Circuits Simulaiton Research

Integer orders differential system is a special case of fractional-order differential system.Integer orders chaotic system that we usually study is ideally approximate to realistic chaoticsystem. Fractional-order chaotic system has broader and changeable values of order and morecomplex dynamical behavior than integer order chaotic system. Thus, fractional-order integer-differential equation can describe the nonlinear characteristics of actual chaotic system moreexactly, which has more prominent research meanings and application value. The thesis aims at aseries of simple to deepgoing study of fractional-order chaotic systems, from monophae fractional-order chaotic system to heterogeneous fractional-order chaotic system, three-dimensionalfractional-order chaos to fractional-order hyperchaos, chaotic system with general phenomenon tochaotic system with special dynamical behavior and etc.(1) The Construction of a three-dimensional Heterogeneous Fractional-order Chaotic Systemand its Multiple Circuits Simulation: Based on integer orders three-dimensional Liu chaotic system,this paper constructs a new three-dimensional heterogeneous fractional-order chaotic system, thatis, the chaotic system’s three-dimensional fractional-orders q take different values (q1=q2=0.9,q3=0.8，in step size of0.1). After analyses this system’s stability and existence, this paper adopts thetree shape, the chain shape and the mixture circuits to conduct experiment simulation on thefractional-order system through Multisim software. The results of multiple circuits’ simulation andMatlab program run have the same chaotic attractor phase diagram. This demonstrates theeffectiveness of this heterogeneous fractional-order chaotic system’s design and provides referablebases for the application in actual circuits.(2) The design and circuit simulation of antistructure fractional-order hyperchaotic Liu syste-m: This antistructure fractional-order hyperchaotic Liu system is a new hyperchaotic oscillationsystem which evolves and forms based on three-dimensional Liu system and it emerges abundantand complex hyperchaotic dynamical behavior in the process of chaotic oscillation. We takeantistructure and add one dimension of two latter equations of primary three-dimensional Liusystem and conduct numerical simulation on it. In the process of circuit realization, we takedifferent values of fractional-order q and adopt chain shape circuit to conduct experimentsimulation. It verifies that this antistructure hyperchaotic Liu system is a hyperchaotic system and itcan be realized by electronic circuit. (3) The Design of a Four-wing Heterogeneous Fractional-order Chaotic System and itsCircuits Simulation: We design a new four-wing four-dimensional heterogeneous fractional-orderchaotic system and its attractors’ moving trajectory can totally present in four-wing shape. Weadopt a nonlinear state feedback controller in electronic circuit experiment simulation and conductexperiment simulation on fractional-order system through software Multisim10.0by adoptingchain shape circuit. At last, we verify the feasibility of state feedback controller in circuit and itprovides referable electronic circuit model to practical circuit application.Three-dimensional heterogeneous fractional-order chaotic system, antistructure hyperchaoticLiu system and four-wing heterogeneous fractional-order chaotic system constructed in thesis allhave commendable dynamical characters. This thesis provides cogent evidence to their practicalcircuit application and provides certain data analyses bases to the study of constructing morecomplex fractional-order hyperchaotic system.