Coupling of neurons favors the bursting behavior and the predominance of the tripod gait

Abstract

In nature, it has been observed that the dominant locomotor pattern of hexapod insects is often the tripod gait. Our analysis of a Central Pattern Generator (CPG) of the insect movement gives reasons for this dominance: the mathematical CPG model presents the tripod pattern with bursting dynamics in a parametric region where an isolated neuron has a simpler behavior. That is, we show how the coupling of small networks of neurons makes the system to continue having bursting dynamics even when an isolated neuron would be spiking. Moreover, in parametric regions where a neuron shows chaotic dynamics, the CPG exhibits a chaotic synchronization phenomenon: the chaotic tripod gait. In other words, coupling loves bursting… and tripod gait. The hyperchaotic phenomenon is also present and we locate regions where up to four Lyapunov exponents are positive.