Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities - Archive ouverte HAL Access content directly
Journal Articles Communications on Pure & Applied Analysis Year : 2022

Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities

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Abstract

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

Dates and versions

hal-03622761 , version 1 (29-03-2022)

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Thierry Horsin, Mohamed Ali Jendoubi. Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities. Communications on Pure & Applied Analysis, 2022, 21 (3), pp.999. ⟨10.3934/cpaa.2022007⟩. ⟨hal-03622761⟩
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