2025/03/17 by Simona Olmi, Antonio Politi, Olmi, Simona +1 · 1 voice
Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #cond-mat.dis-nn #math.DS #nlin.AO #nlin.CD
paper · pdf · doi:10.48550/arxiv.2503.13152
Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space due to the crossing of the boundary of the basin of attraction. We find that crises occur also in non-autonomous systems although the underlying mechanism is more complex. We show that in the vicinity of the transition, the escape probability scales as exp[-α(ln δ)2], where δ is the distance from the critical point, while α is a model-dependent parameter. This prediction is tested and verified in a few different systems, including the Kuramoto model with inertia, where the crisis controls the loss of stability of a chimera state.