New Grid Multi-scroll And Multi-wing Chaotic Systems Generation And Its Circuit Implementation

In the nonlinear science and chaotic circuit area,researching how to produce different types of chaotic and hyperchaotic signals which are suitable for secure communication is a hot issue in recent years,which has a wide range of applications in the neural network,digital watermarking,secure communication and fluid mechanics areas by using their complex topological structure and rich dynamic behavior.Therefore,the study of new and more complex multi-scroll or multi-wing chaotic system becomes a key issue for many engineering applications.This paper briefly analyses the background and significance of chaotic system at home and abroad,concluding the development process of chaotic system,analytical method and chaotic circuit basis of the chaotic system.At the basis of reading a lot of literatures and analyzing the chaos theory,according to more complexity of multi-scroll and multi-wing chaotic systems,two kinds of new grid multi-scroll and multi-wing chaotic systems and circuit implementations of them are carefully proposed.The main work and results of this paper are as follows:1)An approach for generating grid multi-scroll chaotic attractors with multi-block in multi-plane is proposed.Firstly,an appropriate nonlinear function is selected to control the number and direction of scroll chaotic attractors in the newly proposed modified three-order Jerk chaotic system.Then,the new and appropriate control function is added to Jerk system through observing Lyapunov exponent spectrum of relative coefficient and the change of equilibrium points.Many different multi-scroll chaotic attractors with multi-block are generated by adjusting the coefficient of the control function in a plane.The implementation of circuit verifies the feasibility of this method.2)A new approach for generating more complex multi-plane grid multi-wing attractors via novel nonlinear modulating functions is proposed from the firstly presented double-wing generalized Lorenz chaotic system,which breaks the dynamic characteristics limit of the Lorenz system,that multi-wing chaotic systems are still confined in the positive half-space and the threshold limit.By changing the nonlinear function terms and nonlinear function parameters and controlling the relationships between different nonlinear functions,it can produce different multi-plane grid multi-wing chaotic attractors.The proposed method is different from that of classical multi-scroll chaotic attractors,which is generated by square symmetrical multi-segment linear functions and step function combining with sign function.Basic properties of the new system such as dissipation property,equilibrium and stability,the Lyapunov exponent spectrum and bifurcation diagram are analyzed by numerical simulation analysis,which confirm that the multi-wing attractor chaotic system has extremely rich dynamics.Finally,an improved module-based unified circuit is designed for implementation.The circuit experimental results are in good agreements with the numerical simulation results,which provide some principles and guidelines for future circuitry design and engineering application.