Topological invariants in forced piecewise-linear FitzHugh–Nagumo-like systems

Mathematical models for periodically-forced excitable systems arise in many biological and physiological contexts. Chaotic dynamics of a forced piecewise-linear Fitzhugh–Nagumo-like system under large-amplitude forcing was identified by Othmer and Xie in their work [J. Math. Biol. 39 (1999) 139]. Using kneading theory we study the topological entropy of some chaotic return maps associated with a singular system. Finally we introduce a new topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy, that suggest the existence of a relation between the parameters A and θ, when T is fixed.