A dynamic Parrondo’s paradox for continuous seasonal systems

Abstract

We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo's dynamic paradox, in which the stability of an equilibrium, common to all seasons is reversed for the global seasonal system.Mathematics Subject Classification 2010: Primary: 37C75; 34D20. Secondary: 37C25.Keywords: Continuous dynamical systems with seasonality, non-hyperbolic critical points, local asymptotic stability, Parrondo's dynamic paradox.