Analysis, circuit realization and controls of an autonomous Morse jerk oscillator

Abstract

In this paper, an autonomous Morse jerk oscillator which is designed by converting an autonomous two-dimensional Morse oscillator to a jerk oscillator, is analysed. The stability of its unique equilibrium point reveals the existence of Hopf bifurcation. Periodic and chaotic oscillations, antimonotonicity, chaotic bubbles and coexisting attractors are generated in the proposed jerk oscillator. Then, this proposed jerk oscillator is implemented in PSIM software and realized in a printed circuit board to verify the numerical results. The experimental/PSIM results agree well with the numerical simulations. Moreover, it is possible to control partially or totally the amplitude of its signals by introducing two additional parameters in the rate-equations describing the proposed jerk oscillator. Furthermore based on the Routh–Hurwitz conditions and using a single linear feedback controller, the proposed jerk oscillator is controlled to its unique equilibrium point. Finally, the coexistence between periodic and chaotic attractors is destroyed and controlled to a desired trajectory thank to the linear augmentation method.