Extreme events in a forced BVP oscillator: Experimental and numerical studies

Abstract

In this work, we report the existence of extreme events in the well known Bonhoeffer-van der Pol (BVP) oscillator under the excitation of a periodically forced voltage. Extreme events refer to the sudden and random increase in the amplitude of one or more of the state variables of the dynamical system and arise because of the incidence of interior crises or the presence of discontinuous boundaries or intermittency. We have chosen this system because of the fact that it has spawned several systems modelling neuronal dynamics such as Hindmarsh-Rose (HR) and Hodgkin-Huxley (HH) models. Our investigations involve both laboratory experiments and numerical simulations. We have obtained time plots, phase portraits, Poincaré maps, bifurcation graphs, Lyapunov exponents and signal to noise ratio (SNR) to study the general dynamics and to confirm the presence of extreme events, we have used statistical measures such as phase slip analysis, distribution functions for both experimental and numerical data. To the best of our knowledge, we believe that it is for the first time that the occurrence of extreme event has been reported using both real time experimental and numerical studies on this forced BVP system.