Nonlinear System Dynamic Analysis Based On Chaos Entanglement

The investigation of artificial chaotic system is a new subject based on chaotic system,hence artificial chaotic system has much more extensive value in engineering application. Inthis paper, we present a new approach, called chaos entanglement, to generate chaos byentangling two or multiple stable linear subsystems, therefore, it provides an easier way todesign and construct new chaotic attractors by chaos entanglement. Chaos entanglement canbe utilized as a guideline to effectively create artificial chaotic systems in practice.The paper mainly discussed the dynamical anysis of chaotic and structure of System. Thedynamical behaviors of a nonlinear system with three variants (so called chaos entanglementsystem) such as the equilibria, Hopf bifurcation, Chaos Control are investigated. Then thenew chaotic system is proposed in the basis of chaos entanglement system and its dynamicalcharacter is studied through the theoretical anysis. At the same time, the new hyperchaoticsystem is proposed based on chaos entanglement principle, and also the dynamical behaviorof this system are analysed in the round.The main contributions of this paper as follows:(1) The basic dynamical behaviors of a nonlinear system are investigated, which isrecently proposed and called chaos entanglement system. We mainly discussed theparameter’s influence of the system by bifurcation diagram and Lyapunov-exponentsspectrum, which is releavent the single parameter of the system, and each appearance of thissystem in some zone are given in the paper. Besides, we controlled the system to any fixedpoint to eliminate the chaotic vibration by means of sliding mode method. And the numericalsimulations are given to confirm the effectiveness of the controller.(2) Based chaos entanglement system, a new chaotic system with three variants isproposedwhere e is the entanglement coefficient and (sin x, siny,sinz)is the entanglement function, the basic dynamical behaviors of a nonlinear system are investigated by nonlinear dynamicstheory, numerical imitation and circuitry implementation.(3) This paper proposed a new four-dimensional continuous autonomous hyperchaoticsystemwhere e is the entanglement coefficient and (sin x, cosy,sinz,cosw)is the entanglementfunction. The system is constructed based on chaos entanglement principle by introducing aentanglement function. And the dynamical behaviors of this hyperchaoticsystem are furtherinvestigated in detail, including equlibria, stability, various attractors, bifurcation analysis,and Lyapunov-exponents spectrum. Moreover, the chaotic character is verified by theoricalanalysis and number imitation, which analyzed the parameter’s influence of the system.