Early-warning signals for bifurcations in random dynamical systems with bounded noise

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Kuehn, Christian¹  Malavolta, Giuseppe²  Rasmussen, Martin² 

[1] Tech Univ Munich, Fac Math, Boltzmannstr 3, D-85748 Garching, Germany

[2] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

关键词: Bifurcation;    Early-warning signal;    Fast-slow system;    Mixed-mode oscillations;    Random dynamical system;    Set-valued dynamical system;   

DOI  :  10.1016/j.jmaa.2018.03.066

来源: Elsevier

【 摘 要 】

We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal invariant set of the set-valued dynamical system in terms of the derivatives of the so-called extremal maps. We propose an algorithm for reconstructing the derivatives of the extremal maps from a time series that is generated by iterations of the original random dynamical system. We demonstrate that the derivative reconstructed for different parameters can be used as an early-warning signal to detect an upcoming bifurcation, and apply the algorithm to the bifurcation analysis of the stochastic return map of the Koper model, which is a three-dimensional multiple time scale ordinary differential equation used as prototypical model for the formation of mixed mode oscillation patterns. We apply our algorithm to data generated by this map to detect an upcoming transition. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free