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- W4313446756 abstract "Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes in time, and that has been characterized recently using {sc BraMAH} cell complexes and their homology groups. This description has been further improved for their deterministic counterparts by endowing the cell complex with a directed graph, which encodes the order in which the cells in the complex are visited by the flow in phase space. A templex is a mathematical object formed by a complex and a digraph; it provides a finer description of deterministically chaotic attractors and permits their accurate classification. In a deterministic framework, the digraph of the templex connects cells within a single complex for all time. Here, we introduce the stochastic version of a templex. In a random templex, there is one complex per snapshot of the random attractor and the digraph connects the generators or ``holes'' of successive cell complexes. Tipping points appear in a random templex as drastic changes of its holes in motion, namely their birth, splitting, merging, or death. This paper introduces and computes the random templex for the noise-driven Lorenz system's random attractor (LORA)." @default.
- W4313446756 created "2023-01-06" @default.
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- W4313446756 date "2022-12-29" @default.
- W4313446756 modified "2023-10-18" @default.
- W4313446756 title "Random templex encodes topological tipping points in noise-driven chaotic dynamics" @default.
- W4313446756 doi "https://doi.org/10.48550/arxiv.2212.14450" @default.
- W4313446756 hasPublicationYear "2022" @default.
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