Eur. Phys. J. Special Topics 227, 747–756 (2018)
https://doi.org/10.1140/epjst/e2018-800012-7

Regular Article

Stochastic switching in systems with rare and hidden attractors

¹ Department of Applied Cybernetics, St. Petersburg State University, Saint-Petersburg, Russia
² Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, Saratov, Russia
³ Department of Physics, The Technical University of Denmark, Lyngby, Denmark
⁴ Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Dortmund, Germany

^a e-mail: stankevichnv@mail.ru

Received: 31 January 2018
Received in final form: 14 March 2018
Published online: 19 October 2018

Abstract

Complex biochemical networks are commonly characterised by the coexistence of multiple stable attractors. This endows living systems with plasticity in responses under changing external conditions, thereby enhancing their probability for survival. However, the type of such attractors as well as their positioning can hinder the likelihood to randomly visit these areas in phase space, thereby effectively decreasing the level of multistability in the system. Using a model based on the Hodgkin–Huxley formalism with bistability between a silent state, which is a rare attractor, and oscillatory bursting attractor, we demonstrate that the noise-induced switching between these two stable attractors depends on the structure of the phase space and the disposition of the coexisting attractors to each other.