Analysis,Synchronization And Circuit Implementation Of A Three-dimensional Autonomous Chaotic System

Chaotic motion is a special phenomenon of nonlinear systems,which has a rich and complex non-linear dynamics.Since the special applications of chaotic systems in secure communications and biomedicine,constructing a novel chaotic system with new properties and exploring its potential value has become a hot topic in research of nonlinear field.This thesis aims at constructing a chaotic system with some new properties,coupled with the synchronization control of the system,extending wings in one direction,extending wings in two directions into a grid.It also gives the corresponding circuit implementation of the systems by Multisim.This paper proposes a novel three-dimensional autonomous chaotic system.Some properties can be achieved for the system by analyzing Lyapunov exponent spectrum and bifurcation diagrams.The double invariable Lyapunov exponent spectrums are locked when the parameters of the nonlinear terms vary.The amplitude and the phase of the locked chaotic systems can be modulated.These properties of chaotic systems can be certified through theoretical analysis and simulation results.By selecting the appropriate synchronous controller,two chaotic systems with same structure can achieve synchronization.At the same time,this thesis also gives the chaotic circuit,which verifies the consistency of circuit implementation and simulation results by Multisim.The chaotic system has special equilibrium point and the special topology of the chaotic attractor,which can be found through the analysis of the novel chaotic system.The Saddle-Focus balance point of index two in a certain direction can be extended by constructing a suitable non-linear function such as a multi-sectioned square function with even symmetry etc.,and then the new system achieves the extension of multi-wing in one direction.On the basis of the system of one direction multi-wings,we can then construct a ladder wave nonlinear sequence,to achieve the extending of the Saddle-Focus balance point of index two in the other direction,thus to extending the multi-wing chaotic system into a novel grid multi-wing chaotic system.The thesis also gives the synchronization control analysis and the circuit implementation of the multi-wing chaotic system.