Bifurcations and chaos in a two-dimensional discrete Hindmarsh–Rose model

1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model

“…In [21,27], we proved that map (3) possesses flip bifurcation, Neimark-Sacker bifurcation, and 1 : 1, 1 : 2, and 1 : 4 resonance. The aim of this paper is to prove that this discrete model possesses the 1 : 3 resonance.…”

“…Using the Cardan formula (see [28]), we get the following results (see also [8,21] The stability of these fixed points can be found in [21]. In this paper, we focus on the existence and bifurcation analysis of 1 : 3 resonance.…”

“…For example, the transition between spiking and bursting in the model can be understood by homoclinic bifurcations [12,13]. More information on bifurcation can be found in [1,4,[8][9][10][11][14][15][16][17][18][19][20][21][22].…”

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

“…The Hindmarsh-Rose (HR) model is a system of three coupled nonlinear differential equations which can describe the action potential generation of a wide range of neuronal cells [1], [2], [3]. The HR neurons reveal various dynamical behaviors, including spikes, bursting, and chaotic attractors [2], [3].…”

Synchronization in Two Coupled Hindmarsh-Rose Neurons

“…Since Pecora and Carroll (1990) [19] studied synchronization of chaotic systems, chaotic synchronization has been widely used in the secure communication, oscillator networks and neural networks during the last 20 years, see for example, [2,3,4,11,12,13,14,15,16,17,20,22,23,24,25,27,28,29,30].…”