https://doi.org/10.1140/epjst/e2016-02667-x
Regular Article
Strong perturbations in nonlinear systems
The case of stochastic-like resonance and its biological relevance from a complex system's perspective
Université Libre de Bruxelles, Interdisciplinary Center for Nonlinear Phenomena and Complex Systems & Service de Physique des Systémes Complexes et Mécanique Statistique, Bruxelles, Belgium
a Present address: Université Libre de Bruxelles, Dept. of Statistical Physics and Complex Systems, Boulevard du Triomphe 1050 Brussels, Belgium; e-mail: e-mail: vbasios@ulb.ac.be
Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016
A novel case of probabilistic coupling for hybrid stochastic systems with chaotic components via Markovian switching is presented. We study its stability in the norm, in the sense of Lyapunov and present a quantitative scheme for detection of stochastic stability in the mean. In particular we examine the stability of chaotic dynamical systems in which a representative parameter undergoes a Markovian switching between two values corresponding to two qualitatively different attractors. To this end we employ, as case studies, the behaviour of two representative chaotic systems (the classic Rössler and the Thomas-Rössler models) under the influence of a probabilistic switch which modifies stochastically their parameters. A quantitative measure, based on a Lyapunov function, is proposed which detects regular or irregular motion and regimes of stability. In connection to biologically inspired models (Thomas-Rössler models), where strong fluctuations represent qualitative structural changes, we observe the appearance of stochastic resonance-like phenomena i.e. transitions that lead to orderly behavior when the noise increases. These are attributed to the nonlinear response of the system.
© EDP Sciences, Springer-Verlag, 2016
