Controling Switching between Birhythmic States in a New Conductance-based Bursting Neuronal Model

Abstract

A birhythmic conductance-based neuronal model with fast and slow variables is proposed to generate and control the coexistence of two different attracting modes in amplitudes and frequencies. However, periodic bursting, chaotic spiking and bursting haven’t been clearly observed there. The control of bistability is investigated in a three-dimensional birhythmic conductance-based neuronal model. We consider slow processes in neuron materialized by an adaptation variable coupled to system in the presence of an externalinusoidal current applied. By using the harmonic balance method, we obtain the frequency-response curve in which membrane potential resonance with his corresponding frequency are control by varying a specific parameter. At the resonance frequency, bifurcation and lyapunov exponent diagrams versus a control parameter are obtained. They reveal, a coexistence of two different complex attractors namely periodic and chaotic spiking, periodic and chaotic bursting. By using the control parameter as the slow variable, the system can switch from bistable to monostable behavior. This is done by destroying subthreshold (small) oscillation of the neuron. The role of adaptation variable in neuron system is then to filtered many existing electrical processes and permit to adapt the system by the multiple transitions states in the chosen electrical mode. A fairly good agreement is observed between analytical and numerical results.