Diverse Bursting Oscillations in an Asymmetric Memristive Sallen-Key Filter

The asymmetric memristive diode bridge-based Sallen-Key Filter (AMSKF) achieved by introducing an asymmetry diode bridge connected with a capacitor and an inductor to the Sallen-Key Filter, is studied in this paper. Through the analysis of equilibrium point, the stability of the circuit is discussed. Combined with the bifurcation diagram, it can be seen that the negative feedback gain of the Sallen-Key Filter greatly affects the dynamics of the circuit. Diverse dynamical behaviors are discovered by means of phase portraits and Lyapunov exponents, which include six types of typical oscillating behaviors: Period, Quasi-period, Quasi-periodic bursting, Period-2 bursting, Chaotic bursting and Period-1 bursting. Especially, bifurcation mechanisms of various bursting oscillating behaviors are researched by separating the formal equations into two parts, consisting of the fast spiking subsystem and the slow spiking subsystem, based on the fast-slow analysis method. Finally, Multisim experiments are carried out to validate the results of numerical simulations. Compared with the Sallen-Key Filter cascaded with the symmetric memristive diode bridge, the bursting oscillation with larger amplitude and the wider periodic bursting range by adjusting the negative feedback gain are detected.

Automated summary

The paper investigates the asymmetric memristive diode bridge-based Sallen-Key Filter (AMSKF) by connecting an asymmetry diode bridge with a capacitor and an inductor to the Sallen-Key Filter. The stability of the circuit is discussed through equilibrium point analysis, and the dynamics of the circuit is found to be greatly affected by the negative feedback gain of the Sallen-Key Filter, as shown by the bifurcation diagram. Various oscillating behaviors are discovered using phase portraits and Lyapunov exponents, including six types of typical oscillating behaviors. The bifurcation mechanisms of the bursting oscillating behaviors are further researched using the fast-slow analysis method. Multisim experiments are conducted to validate the numerical simulation results, and it is found that the bursting oscillation with larger amplitude and wider periodic bursting range can be detected by adjusting the negative feedback gain compared to the Sallen-Key Filter cascaded with the symmetric memristive diode bridge.