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Global Attractors for a Class of Discrete Dynamical Systems

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Abstract

In this paper, we study the existence of global attractors for a class of discrete dynamical systems naturally originated from impulsive dynamical systems. We establish sufficient conditions for the existence of a discrete global attractor. Moreover, we investigate the relationship among different types of global attractors, i.e., the attractor \({\mathcal {A}}\) of a continuous dynamical system, the attractor \(\tilde{{\mathcal {A}}}\) of an impulsive dynamical system and the attractor \(\hat{{\mathcal {A}}}\) of a discrete dynamical system. Two applications are presented, one involving an integrate-and-fire neuron model, and the other involving a nonlinear reaction-diffusion initial boundary value problem.

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Acknowledgements

The authors would like to thank the anonymous referee for the suggestions that have enhanced this article.

Funding

The first author was partially supported by FAPESP grant 2020/14075-6 and CNPq grant 310540/2019-4. The second author was partially supported by BES-2017-082334.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, São Carlos, SP, 13560-970, Brazil

    Everaldo de Mello Bonotto

  2. Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain

    José Manuel Uzal

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  1. Everaldo de Mello Bonotto
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  2. José Manuel Uzal
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Correspondence to Everaldo de Mello Bonotto.

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E. M. Bonotto: Research partially supported by FAPESP # 2020/14075-6 and CNPq # 310540/2019-4. J. M. Uzal: Research partially supported by BES-2017-082334.

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Bonotto, E.d.M., Uzal, J.M. Global Attractors for a Class of Discrete Dynamical Systems. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-024-10356-9

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  • DOI: https://doi.org/10.1007/s10884-024-10356-9

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