Stability and Chaos Control in a Novel Three-Dimensional Multistable dynamical System with Coexisting Attractors

This paper introduces three-dimensional Continuous-time autonomous dynamical system. We Construct new Lyapunove function for this system, the analysis of stability by new method is consistence with other method of stability. Basic dynamical proper ties such as equilibrium points, dissipativity, multistability, Wave form in time domain, phase portrait, bifurcation and Lyapunov exponents are studied, the analysis indicate that the system is unstable and hyperchaotic with Kaplan york dimension 2.1621. A novel feature of the system has multistability and attraction coexistence for two and three distinct initial condition sets. Also, adaptive control and synchronization system has been created, it is found that the hyperchaotic system achieved good results.