Analyzing Synchronization in a Linear Coupling of Three Chaotic Hindmarsh-Rose Neurons

In this paper we investigate synchronization in three linearly coupled chaotic Hindmarsh-Rose neurons. Specifically, we propose a novel continuous-time dynamical system, which is modeled by a set of nine first-order ordinary differential equations, which was obtained by coupling three chaotic Hindmarsh-Rose neurons. The study considered two cases, namely one in which the coupled systems are identical, and one in which they are non-identical. Regardless of the case considered, the coupling functions are such that the three systems interact through unidirectional couplings, with one of the systems acting as a master system, another acting as an interacting system, and the other acting as a slave system. The investigation was carried out by varying the two parameters related to the coupling strengths, namely β and γ . Regions of partial and complete synchronizations were characterized in (β ,γ ) parameter planes, by using error functions. These results were corroborated by time series plots that consider all nine variables involved in the investigated system, and also by trajectories in the phase-space.