Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect

The design and analysis of simple autonomous memristive circuits are of great significance in theoretical research and practical application of complex dynamics. This paper designs a simple autonomous three-element-based memristive circuit with fast-slow effect, which is constructed by parallel connecting an active second-order memristive diode bridge with a parallel LC filter. The corresponding mathematical model is established, upon which stability analysis of the equilibrium point is performed by Routh-Hurwitz criterion. Theoretical derivation results indicate that the presented memristive circuit is always unstable, and then complex dynamical behaviors of period, chaos, quasi-period, and periodic bursting oscillation are numerically revealed through phase plane orbit, time-domain sequence, Lyapunov exponent spectrum and bifurcation diagram. In addition, bifurcation mechanisms of the periodic bursting behavior are further explored by fast-slow dynamics analysis, from which it can be found that the periodic bursting oscillation of the presented memristive circuit is a type of symmetric fold/Hopf cycle-cycle bursting oscillation. Especially, two types of dynamical behaviors of quasi-periodic oscillation and periodic bursting oscillation with a symmetric fold/Hopf cycle-cycle burster simultaneously appear in such a simple autonomous memristive circuit is amusing, which has never been reported in the previous literatures. (C) 2019 Elsevier Ltd. All rights reserved.