Periodic orbit description of the blowout bifurcation and riddled basins of chaotic synchronization

B.M. Czajkowski and R.L. Viana

Chaos, Solitons & Fractals, 2024, vol. 184, issue C

Abstract: Metric properties of invariant chaotic sets, like chaotic attractors, are closely related to the structure of the unstable periodic orbits embedded in this set. As a system parameter is varied through a critical value, a chaotic attractor lying on an invariant subspace may become transversely unstable, undergoing a blowout bifurcation. We use periodic orbit theory to investigate some of the properties of the blowout bifurcation for a system of two coupled chaotic maps having a synchronized state. We also study riddling of basins associated with chaotic synchronization for this system with the help of periodic orbit theory and a biased stochastic model that uses the properties of the finite-time Lyapunov exponents. The severe breakdown of shadowability of chaotic trajectories due to unstable dimension variability and its relation with the blowout bifurcation are discussed.

Keywords: Blowout bifurcation; Riddled basins; Chaos synchronization; Unstable periodic orbits; Unstable dimension variability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005460

DOI: 10.1016/j.chaos.2024.114994

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