Star-coupled Hindmarsh-Rose neural network with chemical synapses

We analyze the patterns like synchrony, desynchrony, and Drum head mode in a network of Hindmarsh-Rose (HR) neurons interacting via chemical synapse in unidirectional and bidirectional star topology. A two-coupled system has been studied for synchronization by varying the coupling strength and the parameter describing the activation and inactivation of the fast ion channel. The transverse Lyapunov exponent spectrum is plotted to observe the point of transition from desynchrony to synchrony. The synchronized, desynchronized, and drum head mode regions are observed when the neurons are connected in unidirectional and bidirectional coupling configurations. A detailed analysis about the time evolution of membrane potential corresponding to each region is presented. The annihilation of synchronized region and the expansion of drum head mode region in bidirectional coupling is discussed using parameter space. Our work provides finer insight into the existence and stability of Drum head mode and is useful for designing communication networks.