Study of Dynamical Properties and Effective of a State u for Hyperchaotic Pan Systems

89 Study of Dynamical Properties and Effective of a State u for Hyperchaotic Pan Systems Saad Fawzi AL-Azzawi saad_fawzi78@yahoo.com Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq Received on: 27/05/2012 Accepted on: 18/09/2012 ABSTRACT In this paper, we propose a new four-dimensional continuous autonomous hyperchaotic system which is built by adding a nonlinear controller to a threedimensional chaotic Pan system. The new system is analyzed both theoretically and numerically by studying dynamical behaviors for this system, including equilibrium points, Lyapunov exponents, stability and bifurcation, also we study the stability, bifurcation and symmetry for another four dimensional system which is generated by Pan in (2011) from the original system, we compared between two systems and found the difference between them. Finally, we show the effective of state u on the two systems.