Analysis of burst dynamics bound by potential with active areas

Burst firing dynamics that are observed in many neuron models including the Hodgkin-Huxley model, are explained in terms of a motion of a quasi particle bound by potential. We are able to foresee the solution landscape with the curvature of the potential, and can design the wave form of the output to properly set active areas on the potential. In this paper, we apply this concept for a single Hindmarsh-Rose model and a coupled van der Pol oscillators. Therefore, we provide an understanding of the burst firings with spatiotemporal constructions of the potential and the active areas, and claim that the active areas cause the eigen-oscillations individually. Hence, we dispose the active areas on the potential properly and design the intended wave forms. Then, the global curvature of the potential function ensures that these oscillations do not diverge.