CRITICAL-DYNAMICS OF THE BONHOEFFER-VANDERPOL EQUATION AND ITS CHAOTIC RESPONSE TO PERIODIC STIMULATION

We consider the Bonhoeffer-van der Pol equation as a prototype model for excitable systems. For this equation we investigate the effect of application of a periodic stimulus. In a critical range of values for stimulus strength and period we find, depending on the choice of those values, many different response types, which include (quasi)-periodic and chaotic behavior. We present phase portraits and bifurcation diagrams to illustrate these responses. The study of an associated local equation shows that the same types of behavior may be expected in a whole class of related equations. We discuss the relevance of our results for a number of biological and physiological applications.