Chaotic Bursting Behavior of Coupled Neural Oscillators

Abstract

Recently it was shown that dephasing of diffusively coupled neural oscillators leads to a new class of bursting phenomena, where neural oscillators switch between high and low oscillation amplitudes. To analyze this behavior we study a system of three-coupled neurons, which is the most simple one that shows chaotic bursting behavior. For the intermediate values of coupling constant kc, the chaotic bursting behavior occurs. For a quantitative analysis of chaotic bursting, we introduce three mean activities of oscillators. From the Poincaré sections we find a period-doubling route to chaos. We illustrate the busting behavior in terms of competition of the single oscillator behavior with the collective one arising from the diffusive coupling of oscillators.

Bifurcation in coupled BVP neurons with external impulsive forces

“…Although the single neuron without the external force has only one equilibrium point, combining these n (n 2 3) neurons unidirectionally in a ring, n-phase periodic solutions are generated. Applying the impulsive forces, successive period-doubling bifurcations of the n-phase solution occur and chaotic states, namely n-phase chaos, appear.…”

“…Among such firing patterns, synchronous firing of neurons in connection with neuronal signal processing has attracted much interest [3,4]. It is important to consider global dynamics of networks composed of nonlinear neurons in order to clarify not only mechanisms of synchronous firing of neurons but also its functional roles [5].…”

Bifurcation and chaos observed in coupled BVP neurons with external impulsive forces

“…A mong such fi ring patterns, synchronous firing of neu rons in connection with neuronal signal processing has attracted much interest [4,5). It is important to con sider global dynamics of networks composed of non linear neurons in order to clarify not only mechanisms of synchronous firing of neurons but also its functional roles.…”