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

Author

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  • Czajkowski, B.M.
  • Viana, R.L.

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.

Suggested Citation

  • Czajkowski, B.M. & Viana, R.L., 2024. "Periodic orbit description of the blowout bifurcation and riddled basins of chaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005460
    DOI: 10.1016/j.chaos.2024.114994
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