On the stability and Hopf bifurcation of a Shimizu Morioka model Hassan Kamil

Hassan Kamil Jassim

Abstract


This paper presents a three-dimensional continuous autonomous chaotic system is called Shimizu Morioka system (SMS) with four terms and two quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov exponent, and we show that Shimizu Morioka system is almost linear system. Finally, a numerical example is given to support the analytic results.

Keywords


Shimizu Morioka system; Stability, Hopf bifurcation, Almost linear system.

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