Novel Chaotic Systems With Multiple Wings And Their Circuit Designs

The uncertain or unpredictable random phenomena of nonlinear systems under certain conditions are called chaos phenomena.Compared with fixed-wing chaotic systems,the dynamic characteristics of multi-wing chaotic systems are more complex and the realizability of low dimensional systems is better.This thesis studies the dynamic characteristics of three-dimensional multi-wing chaotic systems,synchronization control of chaos and applications in image encryption.The main works of this thesis are as follows:1.A 3D integer chaotic system with multi-wing attractors is constructed based on the conjugate Lorenz-type system.For different values of system's parameters,the systems has chaotic attractors with different topological structures including two-wing,three-wing and four-wing chaotic attractors.The dynamic characteristics of the multi-wing system are analyzed through numerical simulations of phase diagrams,Lyapunov exponents,Poincaré section,diagram bifurcation diagram,etc.An analog circuit of the multi-wing system is designed,simulated by the Multisim and implemented by FPGA(Field Programmable Gate Array,FPGA)circuit.The simulation results of Matlab,Multisim and FPGA are consistent,which verifies the system's chaotic characteristics and realizability.An adaptive sliding mode synchronous controller is designed.With the introduction of designed controller,the given signals can be tracked within 0.25 s and the unknown parameters can be identified within 0.12 s.2.Based on the constructed 3D integer chaotic system with multi-wing attractors,a3 D fractional chaotic system with multiple wings is designed.The most important feature of the system is that there is a coexistence of multiple types of multi-wing chaotic attractors,namely the coexistence of two-wing,three-wing and four-wing chaotic attractors.The system's dynamic characteristics are analyzed via numerical simulations of phase diagram,Lyapunov exponent spectrum,Poincaré section,bifurcation diagram,etc.A necessary condition for the existence of chaotic attractors is obtained,namely q > 0.8224.For fixed values of system parameters,given q = 0.98,there is a coexistence of two-wing,two-wing and four-wing chaotic attractors in the system;given q = 0.83,the two-wing,three-wing and four-wing chaotic attractors coexist,which shows that the chaotic characteristics of the system are complex.Thesimulation results of an analog circuit of the system by the Multisim are consistent with those by the Matlab numerical analysis,which further verifies the system's chaotic behaviors.The fractional-order Lyapunov stability theory is used to perform adaptive synchronization control of the system.The simulation results show that the controller is effective.3.The constructed 3D integer order chaotic system with multi-wing attractors is applied to image encryption.A pseudo-random sequence generator based on the chaotic system is constructed and then a chaotic sequence is obtained.The sequence's tests of frequency distribution and randomness are passed,which indicates that the sequence has good random characteristics.The successfully-tested multi-wing chaotic sequence is applied to image encryption,which indicates the system's applicability in image encryption.