Effect of dynamic coupling in an inferior olive neuron model and synchronization

Abstract

In this paper, we use the idea of dynamic coupling to describe the effect of drugs or chemical substances on the electrophysiological properties of the inferior olive neuron (ION). Therefore, a six-dimensional dynamically coupled Kazantsev master–slave configuration of the ION is obtained. In this configuration, the master and slave subsystems have an indirect interaction, and they are not connected through common signals; instead, the slave subsystem receives a coupling signal, which is dynamically generated by a second order linear system. This type of coupling is called dynamic coupling and enables us to take into consideration the state of the medium through which the master and slave are interconnected. The dynamical behavior of the new model is analyzed analytically using limit cycle prediction and numerically via the two-dimensional bifurcation diagrams with respect to two essential bifurcation parameters of the model. Taking the nonlinear function parameter a and two parameters from the coupling subsystem, the adaptive coupling parameter γ2 and the master–slave coupling strength b, as essential bifurcation parameters, the results show that a change of one of these parameters gives rise to complex dynamics such as periodic oscillations, period doubling scenarios, and chaotic states characterized by spike-bursting. Assuming two coupled neurons with parameter mismatch, it is observed that an increase in the external coupling strength ɛ1 favors their synchronization. Furthermore, the analog circuit of the complete new model confirms the burst analysis and the existence of chaos in the model.