Design And Analysis Of Chaotic Attractors With Complex Topological Structures

Chaos is a pseudo random phenomenon which is sensitive to initial conditions in the nonlinear deterministic system.In the past few decades,chaos makes great progress and shows broad application prospects in hydrodynamics,social economic,neural network,population ecology and biomedicine and so on.Especially in the secure communication field,the higher complexity of chaotic system is helpful to improve the security of communication system.In view of this,this thesis designs and analyzes the chaotic attractors with complex topological structures and the main contents are as follows.In the aspect of scroll chaotic attractors,based on a third-order linear autonomous system,state feedback controllers are introduced to construct a higher-order linear system,and in the constructed higher-order system,piecewise linear switching functions,such as stair function and saturation function,are introduced to generate high-dimensional grid scroll attractors.Furthermore,some dynamics characteristics of the high-dimensional multi-scroll system are investigated,including its equilibrium points,dissipation,Lyapunov exponents and bifurcation diagram,etc..In the aspect of wing chaotic attractors,based on a double wing Lorenz-like system,rotation transformation is applied to make sure that its saddle-focus equilibrium points with index 2 are located on the plane y(28)0,and translation transformation and mirror reflection conversion are implemented on the rotation transformed system to extend wing attractors along the x-axis direction,and finally,stair switching functions are introduced into the state variables y and z to generate three-dimensional grid wing attractors.Furthermore,some dynamics characteristics of the three-dimensional multi-wing system are investigated,including its equilibrium points,dissipation,Lyapunov exponents and bifurcation diagram,etc.,and the corresponding circuit is designed.Finally,the main contents of this thesis are summarized and the prospects of future work are put forward.