2018/11/09 by Yuzuru Sato, Thai Son Doan, Sato, Yuzuru +5 · 3 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Earth Systems and Cosmic Evolution #Ecosystem dynamics and resilience #Mathematical Dynamics and Fractals #nlin.CD
paper · pdf · doi:10.48550/arxiv.1811.03994
arxiv created 2018/11/09 · arxiv updated 2018/11/12
The emergence of noise-induced chaos in a random logistic map with bounded noise is understood as a two-step process consisting of a topological bifurcation flagged by a zero-crossing point of the supremum of the dichotomy spectrum and a subsequent dynamical bifurcation to a random strange attractor flagged by a zero crossing point of the Lyapunov exponent. The associated three consecutive dynamical phases are characterized as a random periodic attractor, a random point attractor, and a random strange attractor, respectively. The first phase has a negative dichotomy spectrum reflecting uniform attraction to the random periodic attractor. The second phase no longer has a negative dichotomy spectrum - and the random point attractor is not uniformly attractive - but it retains a negative Lyapunov exponent reflecting the aggregate asymptotic contractive behaviour. For practical purposes, the extrema of the dichotomy spectrum equal that of the support of the spectrum of the finite-time Lyapunov exponents. We present detailed numerical results from various dynamical viewpoints, illustrating the dynamical characterisation of the three different phases.