Control of a dendritic neuron driven by a phase-independent stimulation

Abstract

A dendritic neuron model exhibits bistability under continuous weak stimulation – the oscillatory synchronized regime and the quiet regime coexist. Complex nonlinear dynamics is observed when the neuron undergoes not only phase-dependent continuous weak stimulation, but also when it is driven by an external phase-independent stimulation. In the latter case basin boundaries between the synchronized and the quiet regime become complex and fractal. Simple strategies based on control pulses are not sufficient in these circumstances, because it becomes difficult to predict the dynamics of the neuron after the application of the control pulse. Therefore, a new neural control method is proposed. Initially, a weak phase control strategy is applied until fractal basin boundaries evolve into a deterministic manifold. Consequently, a single control pulse is immediately applied and the neuron evolves into the calm state.