Negative Feedback Mediated by Fast Inhibitory Autapse Enhances Neuronal Oscillations Near a Hopf Bifurcation Point

Author:

Jia Bing1ORCID

Affiliation:

1. State Key Laboratory of Medical Neurobiology, Department of Physiology and Biophysics, School of Life Sciences, Collaborative Innovation Centre for Brain Science, Fudan University, Shanghai 200438, P. R. China

Abstract

One-parameter and two-parameter bifurcations of the Morris–Lecar (ML) neuron model with and without the fast inhibitory autapse, which is a synapse from a neuron onto itself, are investigated. The ML neuron model without autapse manifests an inverse Hopf bifurcation point from firing to a depolarized resting state with high level of membrane potential, with increasing depolarization current. When a fast inhibitory autapse is introduced, a negative feedback or inhibitory current is applied to the ML model. With increasing conductance of the autapse to middle level, the depolarized resting state near the inverse Hopf bifurcation point can change to oscillation and the parameter region of the oscillation becomes wide, which can be well interpreted by the dynamic responses of the depolarized resting state to the inhibitory current stimulus mediated by the autapse. The enlargement of the parameter region of the oscillation induced by the negative feedback presents a novel viewpoint different from the traditional one that inhibitory synapse often suppresses the neuronal oscillation activities. Furthermore, complex nonlinear dynamics such as the coexisting behaviors and codimension-2 bifurcations including the Bautin and cusp bifurcations are acquired. The relationship between the bifurcations and the depolarization block, a physiological concept that indicates a neuron can enter resting state when receiving the depolarization current, is discussed.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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