Extremely slow passages in low-pass filter-based memristive oscillator

Abstract

Slow passage effect in a nonlinear dynamical system commonly generates a delay in the bifurcation point, which can cause an uncertainty in the prediction of dynamics around the bifurcation point. This paper presents a simple memristive oscillator achieved by linking a second-order memristive diode bridge to the in-phase input of a Sallen-Key low-pass filter (LPF). The dynamics of the simple memristive oscillator highly depends on the negative feedback gain of the LPF. Abundant dynamical behaviors are revealed, which mainly include two types of oscillating behaviors: general periodic and quasi-periodic oscillations as well as special periodic, quasi-periodic, chaotic and chaotic 2-torus bursting oscillations. Particularly, an interesting phenomenon of extremely slow passage is found in these bursting oscillations. Through constructing Hopf bifurcation set of the fast spiking subsystem, bifurcation mechanisms of various bursting oscillating behaviors with such extremely slow passages are explored. In addition, Multisim simulations and circuit experiments are performed to validate the numerical simulations.