Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings

Influence of external current and noise on modes of electrical activities and energy of Hindmarsh-Rose model coupled by memristive synapses

“…The synchronization factor (8) is a special case to measure the collective behavior in neuronal network; there are other type of tools to measure that collective behavior. For instance to measure phase synchronization between neurons in the system, we can use the Kuramoto parameter [30]. That KURAMOTO parameter has been introduced by Pikovsky et al [31] where it is defined as the norm of the complex mean field.…”

Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg–Landau equation

“…In this paper, following Refs. [3,4] we generalize the HR neural model assuming only that the coupling between neural oscillators are long-ranged through the membrane potential variable. The HR neural network is then assumed as a system of N neural oscillators in which the configuration of couplings is assumed to be power long-ranged.…”

“…Interestingly, the recent work by Kakmeni et al reported on the presence of these waves of the nerve impulse in diffusive Hindmarsh-Rose (HR) neural networks with nearest-neighbor couplings [3]. Also, as recently demonstrated, the dynamics of an individual neuron in diffusive HR neural networks may be influenced by the interaction or coupling with other neurons [4,5]. It would be interesting now to see what are the effects that the long-range diffusive coupling or interaction has on the wave propagation in such a network.…”

Bifurcation analysis of a two-dimensional discrete Hindmarsh–Rose type model

“…Yu and Cao [9] presented the existence of one-parameter bifurcations of three-dimensional discrete Hindmarsh-Rose, and numerical simulations were given to illustrate the bifurcation analysis. One can find more information on bifurcations of the Hindmarsh-Rosetype model in [10][11][12][13][14][15][16][17][18] and on related one(two)-parameter bifurcation theory in [19][20][21][22][23][24][25][26][27]. Herein, we discuss the following revised model [28] in 2007:…”