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Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects
Zhilong He1, Chuandong Li2, Ling Chen2
1Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China; School of Finance, Xinjiang University of Finance and Economics, Urumqi, 830012, PR China.
Abstract:
In present work, in order to reproduce spiking and bursting behavior of real neurons, a new hybrid biological neuron model is established and analyzed by combining the FitzHugh-Nagumo (FHN) neuron model, the threshold for spike initiation and the state-dependent impulsive effects (impulse resetting process). Firstly, we construct Poincaré mappings under different conditions by means of geometric analysis, and then obtain some sufficient criteria for the existence and stability of order-1 or order-2 periodic solution to the impulsive neuron model by finding the fixed point of Poincaré mapping and some geometric analysis techniques. Numerical simulations are given to illustrate and verify our theoretical results. The bifurcation diagrams are presented to describe the phenomena of period-doubling route to chaos, which implies that the dynamic behavior of the neuron model become more complex due to impulsive effects. Furthermore, the correctness and effectiveness of the proposed FitzHugh-Nagumo neuron model with state-dependent impulsive effects are verified by circuit simulation. Finally, the conclusions of this paper are analyzed and summarized, and the effects of random factors on the electrophysiological activities of neuron are discussed by numerical simulation.
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