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Perturbation of a Globally Stable Steady State and Uniform Persistence

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Abstract

In this paper we consider a parametrized family of semi-flows with continuous or discrete time. In the spirit of the global stability result proved by Smith and Waltman (Proc AMS 127:447–453, 1999) we use the upper semi-continuity of a parametrized family of global attractors. Here we investigate the case where the linearized equation of the unperturbed system has a simple dominant eigenvalue 0 in the case of a continuous time system (or 1 in the case of a discrete time system). New difficulties arise since such a system may exhibit a bifurcation. The goal of the paper is to describe the global dynamics of the perturbed system.

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  1. Faculte des Sciences et Techniques, B. P. 540, 76058, Le Havre, France

    Pierre Magal

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Magal, P. Perturbation of a Globally Stable Steady State and Uniform Persistence. J Dyn Diff Equat 21, 1–20 (2009). https://doi.org/10.1007/s10884-008-9127-0

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  • DOI: https://doi.org/10.1007/s10884-008-9127-0

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