Chaotically spiking canards in an excitable system with 2D inertial fast manifolds

Phys Rev Lett. 2007 Feb 16;98(7):074104. doi: 10.1103/PhysRevLett.98.074104. Epub 2007 Feb 13.

Abstract

We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically but deterministically triggers excitable spikes. This scenario is also found in a model for a nonlinear Fabry-Perot cavity with one pendular mirror.