https://doi.org/10.1140/epjs/s11734-025-02037-5
Regular Article
Analysis of stochastic sensitivity of transient attractors in excitable systems
Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina 51, 620000, Ekaterinburg, Russian Federation
Received:
8
August
2025
Accepted:
17
October
2025
Published online:
2
November
2025
We consider a problem of analyzing the dispersion of random trajectories of nonlinear dynamical systems in the regime of stochastic excitement. Excitability is explained by the presence of metastable states that temporarily attract solutions of unforced deterministic systems. These metastable states form transient attractors, which play a key role in the formation of complex stochastic oscillations of large amplitudes even in equilibrium systems. Dispersion of these oscillations is defined by the stochastic sensitivity of transient attractors. In this paper, a mathematical theory of stochastic sensitivity of transient attractors is constructed for the first time. The analytical capabilities of this new constructive theory are demonstrated using examples of excitable models of Morris–Lecar and FitzHugh–Nagumo.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
