Stochastic basin stability in complex networks

¹ Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University - Shanghai 200433, PRC
² Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education - Shanghai, PRC
³ Potsdam Institute for Climate Impact Research (PIK) - 14473 Potsdam, Germany
⁴ School of Mathematical Sciences and Shanghai Center for Mathematical Sciences, Fudan University Shanghai, 200433, PRC
⁵ Department of Physics, Humboldt University - 12489 Berlin, Germany

Received: 4 May 2018
Accepted: 6 June 2018

Abstract

In this paper, we propose a novel concept, stochastic basin stability, to investigate the stability of dynamical systems under random noises. By this concept, we investigate synchronization of multistable second-order Kuramoto models under continuously acting perturbations in complex networks. By a mean-field approach and the Fokker-Planck equation, we derive formulas of the density functions of both phase and frequency. Based on them, we provide an analytical treatment of stochastic basin stability and illustrate that the theoretical results are in good agreement with numerical simulations. This proposed concept integrates the perturbations of both initial condition and random intervention, and paves a general and efficient approach for analytically and numerically investigating stability of stochastic dynamical systems.