Dynamics of a simple third-order autonomous MLC circuit

Abstract

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.

A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

“…Bifurcation analysis is a useful tool to understand the qualitative properties of chaotic systems ( [15], [16]). Antimonotonicity of a dynamical system refers to the creation of period doubling followed by their annihilation via period-doubling bifurcation, which is an active research topic for chaotic systems ( [17], [18]). Multistability for a nonlinear dynamical system refers to the coexistence of chaotic attractors for a fixed set of parameter values but different sets of values for the initial states of the dynamical system ( [16], [19]).…”