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Chaotically spiking canards in an excitable system with 2D inertial fast manifolds
Francesco Marino1, Francesco Marin, Salvador Balle
1Dipartimento di Fisica, Università di Firenze, INFN, Sezione di Firenze, and LENS, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy.
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.
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