Symmetric periodic bursting behavior and bifurcation mechanism in a third-order memristive diode bridge-based oscillator

This paper presents a novel third-order autonomous memristive diode bridge-based oscillator with fast-slow effect. Based on the modeling of the presented memristive oscillator, stability of the equilibrium point is analyzed by using the eigenvalues of the characteristic polynomial, and then symmetric periodic bursting behavior is revealed through bifurcation diagrams, phase plane plots, time sequences, and 0-1 test. Furthermore, bifurcation mechanism of the symmetric periodic bursting behavior is explored by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem with the variations of the system parameter and slow-scale variable. Consequently, the presented memristive oscillator is always unstable and exhibits complex dynamical behavior of symmetric periodic bursting oscillations with a symmetric fold/Hopf cycle-cycle burster. In addition, experimental measurements are performed by hardware circuit to confirm the numerical simulations.