Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity

Abstract

We prove the existence of multiple periodic solutions as well as the presence of complex profiles (for a certain range of the parameters) for the steady state solutions of a class of reaction diffusion equations with a FitzHugh-Nagumo cubic type nonlinearity. An application is given to a second order ODE related to a myelinated nerve axon model

Complex Dynamics in One‐Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

“…Similar examples of complex dynamics for the Poincaré map associated with differential systems have been discussed, e.g., in [61][62][63][64][65], using different methods. See also [1,31,66] for recent contributions in this direction. Now we are in position to state our main result for (17).…”

“…where ( ) is the so-called 1-periodic "sawtooth function". Analogous investigations have been addressed also in [30,31].…”