Publication Type

Journal Article

Journal Name

Nonlinear Dynamics

Publication Date

1-1-2016

Abstract

In this paper, we investigate the dynamics of two coupled bursting neurons. The Hindmarsh–Rose mathematical model of the neuron subjected to an external periodic stimulus is considered. We transform this model into that of the one-dimensional problem of a particle driven by a periodic external force under the influence of a double-well potential. We study the bifurcation structures, chaotic behavior, and the synchronization dynamics of the transformed model. Numerical simulations reveal the existence of some bifurcation structures including saddle-node, symmetry-breaking, and period-doubling route to chaos. By varying the system’s parameters, we also find thresholds for which the system remains periodic. In Lyapunov exponent diagrams, regions of chaos, quasi-periodicity, and periodicity are clearly identified. In the synchronization dynamics, the Lyapunov function criteria is used to determine the stability of the synchronized states. In addition, the threshold parameters for which the synchronization occurs have been found. The synchronization energy of the coupled model is derived using the generalized Hamiltonian formalism. It is shown that maintaining the system in a synchronized regime requires a nonzero flow of energy per unit time.

Keywords

Bursting neurons, Chaos synchronization, Lyapunov function, Synchronization energy

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