Pattern transition and bifurcation analysis of ELU-type memristive FitzHugh-Nagumo neuron

The memristive neuron model exhibits complex and unpredictable dynamical behavior, especially in the transition of firing patterns, which poses significant challenges for studying the firing mechanisms of neurons. To better explore the different firing activities of memristive neurons, an ELU-type memristive FitzHugh-Nagumo neuron model based on the ELU activation function, which addresses the issue of gradient vanishing effect, is proposed firstly. The equilibrium points of the model are investigated for initial exploration, leading to the understanding of the causes of firing phenomenon and its transition. To further elucidate the firing mechanism triggered by external stimulation, an exhaustive characterization of complex bifurcation behaviors and phase trajectory is provided through a novel semi-analytical perspective, capturing the evolution of both stable and unstable firing activities, particularly the migration from unstable to stable firing patterns. Additionally, Hamilton energy derivatives with time and attractor control, such as amplification and offset-boosting controls, are applied to reflect the arbitrary relocation of the dynamics. The mode shift of unsteady and steady periodic attractors and the accuracy of implicit discrete mapping method are verified by field-programmable gate array.