Design Of A Multi-Wing Chaotic System With One Equilibrium And Research Of Fractional-Order Chaotic Synchronization

Chaos,which is widely existed in nonlinear systems,is a kind of special dynamics.The features that it is unpredictable,bounded,stable and highly sensitive to the initial conditions make chaos be widely used in natural sciences,electronic communication,biological sciences and any other fields.The more complex the dynamics of the chaotic attractor are,the higher confidentiality the chaotic system is.The simpler the structure of chaotic system is,the easier it is applied in engineering.Therefore,it has been a hot pot for us to design simple systems with rich dynamics.In order to take advantage of the chaos,we also need to make the chaotic system easily controlled.As a result,the study of chaotic synchronization is also necessary.This paper briefly introduces the emergence and development of chaotic theory.Besides,some typical chaotic systems,as well as some typical methods for fractional chaotic synchronization which are studied in recent years have been introduced.On this basis,the paper completed the following research.The main contributions and works are concluded as follows:1)First of all,a novel four-dimensional smooth system is presented.What particularly interests us is that the novel multi-wing chaotic system has only one equilibrium point at the origin.Furthermore,the strange phenomenon that different chaotic attractors such as the two-wing,three-wing chaotic attractors and four-wing hyperchaotic attractor could be generated by changing a single system parameter makes this system unique.Secondly,by applying either analytical or numerical methods,basic properties of the system such as phase portraits,Poincare mapping,bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions.At last,according to the theory of chaotic circuit designation,an oscillator circuit with variable resistance is designed.By changing the resistance,we obtain different kind of attractors,which are completely agree with the numerical simulations.The physical existences of the multi-wing chaotic attractors are verified by an electronic circuit.2)The problem of chaotic synchronization between two fractional-order chaotic systems is studied.Based on the fractional-order stability theorem,new approaches to synchronization between two fractional-order chaotic systems with the same order or different orders are proposed,which could greatly simplify the design of synchronization controller.Based on these new methods,the corresponding synchronization controllers are designed,assuring that fractional order chaotic oscillators can be synchronized.Theoretical analysis and numerical simulations certify effectiveness of the method.