Dynamics of a simple third-order autonomous MLC circuit

This paper reports a new simple third-order memristive circuit only containing three elements of inductor, capacitor, and active generalized memristor, from which rich dynamical behaviors are generated. With a dimensionless system model, the performed analyses show that the proposed memristive circuit only has an unstable equilibrium point of saddle-focus-type. The antimonotonicity makes the system exhibits coexisting chaotic and periodic bubbling single-parameter bifurcation routes. Moreover, the quasiperiodic torus, various bursting and beat phenomena with chaotic and periodic oscillations are demonstrated by numerical simulations. The analog circuit implementations are further presented to show the phase portraits and time sequences of the generated attractors.