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Asymptotics for some discretizations of dynamical systems, application to second order systems with nonlocal nonlinearities

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Thierry Horsin
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  • PersonId : 1049798
Mohamed Ali Jendoubi
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  • PersonId : 879412

Abstract

In the present paper we study the asymptotic behavior of discretized finite dimen- sional dynamical systems. We prove that under some discrete angle condition and under a Lojasiewicz’s inequality condition, the solutions to an implicit scheme con- verge to equilibria points. We also present some numerical simulations suggesting that our results may be extended under weaker assumptions or to infinite dimensional dynamical systems.
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Dates and versions

hal-03278131 , version 1 (05-07-2021)
hal-03278131 , version 2 (19-07-2021)

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  • HAL Id : hal-03278131 , version 2

Cite

Thierry Horsin, Mohamed Ali Jendoubi. Asymptotics for some discretizations of dynamical systems, application to second order systems with nonlocal nonlinearities. 2021. ⟨hal-03278131v2⟩
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