Dynamic Analysis And Circuit Design Of New Chaotic Systems

Chaos,as a unique form of motion in nonlinear dynamical systems,exists widely in biology,physics,geology and medicine.Hidden attractor,as a new type of attractors,has aroused the interest of researchers because of its important applications in theoretical research and engineering.The coexistence of hidden attractors is the phenomenon of multiple hidden attractors coexisting,which can provide more flexibility for engineering applications.This paper mainly conducts a comprehensive dynamic analysis of the proposed new 4D chaotic systems with coexisting hidden attractors.The main research work is as follows:A new 4D chaotic system with infinite equilibria is proposed by using a linear state feedback controller in the classical Sprott C system.The dynamic characteristics of the new chaotic system are fully analyzed from the aspects of phase portraits,bifurcation diagram,Lyapunov exponents and Poincare map.Although the new 4D chaotic system has only two nonlinear terms,it has rich dynamic characteristics,such as hidden attractors and coexisting attractors.The corresponding analogue electronic circuit is designed and implemented to verify the feasibility of the new 4D chaotic system.By taking advantage of the complex dynamic properties of the new chaotic system,a random number generator algorithm is proposed.The results of NIST-800-22 test show that the sequence generated by the algorithm has good randomness.Based on the Rucklidge system,using state feedback control technology,a new 4D chaotic system with self-excited attractor or hidden attractor is introduced.The self-excited attractor and the hidden attractor are depending on the parameter of the new 4D chaotic system.There are different kinds of coexisting asymmetric attractors in the new 4D chaotic system,and the dynamical properties of the proposed new 4D chaotic system have been vividly demonstrated in terms of phase portraits,bifurcation diagrams and Lyapunov exponents.Besides,the corresponding circuit of the 4D chaotic system is designed to verify its feasibility,concurrently,the random number generator and the image encryption algorithm based on the proposed new 4D chaotic system are provided.The experimental results show that the sequence generated by the random number generator has sufficient randomness,and the image encryption algorithm has acceptable security.