Switching motion analysis and synchronization control of a locally active memristive neuron model

In this paper, a new four-dimensional HR neuron model is developed by means of injecting external alternating current and introducing a locally active memristor to simulate the induced current in the synapse. Firstly, the stableness of the equilibrium points under alternating current injection is analyzed by using Matlab software, and it is found that the addition of alternating current makes the stableness distribution of equilibrium points vary between time intervals. Secondly, with the help of bifurcation diagrams and corresponding time response diagrams, the effect of induced current on the boundary dynamic behavior is investigated in detail, meanwhile, the conditions for switching motions on separated boundaries are revealed. Finally, the multi-neuron coupling synchronization is explored by setting the corresponding coupling model. The results are beneficial to understand the boundary dynamic mechanism of neurons.