Stability properties of nonlinear dynamical systems and evolutionary stable states

•We address the problem of equilibrium stability in a general class of non-linear systems.•We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems.•We show that an interior ES point may be related to stable interior fixed points of QP systems. In this...

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Bibliographic Details
Published in:Physics letters. A 2017-03, Vol.381 (11), p.954-957
Main Authors: Gleria, Iram, Brenig, Leon, Rocha Filho, Tarcísio M., Figueiredo, Annibal
Format: Article
Language:English
Subjects:
Evolutionary stable states
Non-linear systems
Quasi-Polynomial systems
Stability
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Summary:•We address the problem of equilibrium stability in a general class of non-linear systems.•We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems.•We show that an interior ES point may be related to stable interior fixed points of QP systems. In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2017.01.029