A neural memristor system with infinite or without equilibrium

Memristor has been investigated in dynamical systems. Due to the ionic transportation from extracellular and intracellular, the induction current is excitable in neuron with ion-channels based on the electromagnetic effect. A neural memristor system is reconstructed when the induction current is considered. Furthermore, the dynamical behaviors are calculated by the mathematical approaches, including the bifurcation diagram, time series, and equilibrium point analysis. It is found that the neural memristor system has the infinite equilibrium and no-equilibrium when a bifurcation parameter varies. For the neural model with memristor, its dynamical behaviors can transit from multi-period attractor into strange attractor with varying the bifurcation parameter. It is important to point out that the memory interplay between membrane potential and induction current depends on the initial magnetic flux