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- W3115348585 abstract "Although mathematical models do not fully match reality, robustness of dynamical objects to perturbation helps bridge from theoretical to real-world dynamical systems. Classical theories of structural stability and isolated invariant sets treat robustness of qualitative dynamics to sufficiently small errors. But they do not indicate just how large a perturbation can become before the qualitative behavior of our system changes fundamentally. Here we introduce a quantity, intensity of attraction, that measures the robustness of attractors in metric terms. Working in the setting of ordinary differential equations on $mathbb{R}^n$, we consider robustness to vector field perturbations that are time dependent or independent. We define intensity in a control-theoretic framework, based on the magnitude of control needed to steer trajectories out of a domain of attraction. Our main result is that intensity also quantifies the robustness of an attractor to time-independent vector field perturbations; we prove this by connecting the reachable sets of control theory to isolating blocks of Conley theory. In addition to treating classical questions of robustness in a new metric framework, intensity of attraction offers a novel tool for resilience quantification in ecological applications. Unlike many measurements of resilience, intensity detects the strength of transient dynamics in a domain of attraction." @default.
- W3115348585 created "2021-01-05" @default.
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- W3115348585 date "2022-04-25" @default.
- W3115348585 modified "2023-10-17" @default.
- W3115348585 title "Intensity---A Metric Approach to Quantifying Attractor Robustness in ODEs" @default.
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- W3115348585 doi "https://doi.org/10.1137/20m138689x" @default.
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