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- W2169189229 abstract "Computers are used extensively to simulate continuous dynamical systems. However, different conceptual and mathematical structures underlie discrete machines and continuous dynamics, so the question arises as to the ability of the computer to simulate or, more generally, to check the properties of a continuous system. We discuss and compare two notions of stability for a continuous dynamical system, viz. shadowing and robustness, and relate them to both the practical and theoretical computability of the system. We first discuss what we can learn from the stability of a system, using a finite-precision machine. We then show, following the work in Collins (2005), that shadowing fails but robustness succeeds in ensuring the checkability of a reachability property." @default.
- W2169189229 created "2016-06-24" @default.
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- W2169189229 date "2007-04-01" @default.
- W2169189229 modified "2023-09-26" @default.
- W2169189229 title "Dynamical systems: stability and simulability" @default.
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- W2169189229 doi "https://doi.org/10.1017/s096012950700597x" @default.
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