Switching Dynamics of a FitzHugh-Nagumo Circuit

In this chapter, the nonautonomous FitzHugh-Nagumo neuronal circuit with piecewise memristor is investigated in flux-charge domain through the theory of switching flow. The sufficient and necessary conditions of switching motions, such as passable and grazing on the boundary, are developed to understand the switching mechanism. The switching bifurcation diagrams with changing the system parameters and initial conditions are studied to reveal the hidden extreme multistability and coexisting attractors. The parameter mappings and basins of attractor are also carried out to express the coexistences of periodic orbits and chaos with different mapping structures. The simulation results show that the switching and grazing motion are verified the effectiveness of the analytical conditions.