2018/03/01 by Christian Kuehn, Kuehn, Christian, Giuseppe Malavolta +3 · 1 citation
Environmental Science · #37C70 #37G35 #37H20 #49K21 #70K70 #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1803.00382
openalex publication_date 2018/03/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider discrete-time one-dimensional random dynamical systems with\nbounded noise, which generate an associated set-valued dynamical system. We\nprovide necessary and sufficient conditions for a discontinuous bifurcation of\na minimal invariant set of the set-valued dynamical system in terms of the\nderivatives of the so-called extremal maps. We propose an algorithm for\nreconstructing the derivatives of the extremal maps from a time series that is\ngenerated by iterations of the original random dynamical system. We demonstrate\nthat the derivative reconstructed for different parameters can be used as an\nearly-warning signal to detect an upcoming bifurcation, and apply the algorithm\nto the bifurcation analysis of the stochastic return map of the Koper model,\nwhich is a three-dimensional multiple time scale ordinary differential equation\nused as prototypical model for the formation of mixed-mode oscillation\npatterns. We apply our algorithm to data generated by this map to detect an\nupcoming transition.\n