Hopf Bifurcation and Chaos in a General Jerk System with Arbitrary Desired Odd Number of Equilibria

This paper investigates Hopf bifurcation and chaos in a general jerk system with arbitrary desired odd number of equilibria. First, we get the exact number of equilibria by using monotonicity, extremum and the zero point theorem. Moreover, the stabilities of the equilibria are analyzed. Second, the Hopf bifurcation at equilibria is analyzed and the approximate expression and stability of the bifurcating periodic orbit are given. Third, we find that the system with arbitrary odd number of equilibria could also have chaotic attractors. The corresponding Lyapunov exponent spectrum is given.