Bifurcation Analysis of a System of Morris- Lecar Neurons with Time Delayed Coupling

Abstract

In this study, we consider two coupled Morris-Lacer neurons and study the effect of time delay(t) on the behavior of neuron via electrical coupling. This study focuses on the effects that the electrical coupling strength (g), and Leakage conductance of the membrane ( ) causes on the dynamics of the system. Stable states of the system are determined with respect to g and t using the appropriate phase models, and the regions of validity of the phase models in the membrane voltage signal against axonal distance plane using finite difference method estimated. Analysis of electrical coupling strength and specific membrane capacitance are analyzed. When the value of electrical coupling strength is less, it indicates a higher response to the variation of membrane voltage signal. As the electrical coupling strength increases, the voltage of the neurons decreases. When the axonal distance (x) increases, specific membrane capacitance C, also increases to optimum level then decreases after attaining axonal distance of 4nm. This shows that with appropriate choice of the voltages of g the neurons can be made arbitrarily close in finite time and will remain that close for all subsequent time. As the current density is increased the amplitude of stable periodic responses decreases into a stable fixed point which is determined by both calcium and potassium ions. The results obtained were presented graphically and discussed.