Flows in \(\mathbb {R}^2_+\) without interior fixed points, global attractors and bifurcations

Original Paper

Abstract

In this paper, we study continuous flows \(\varphi :\mathbb {R}^2_+\times \mathbb {R}\rightarrow \mathbb {R}^2_+\) without interior fixed points. We focus on dissipative flows and find some necessary and sufficient conditions for the global attractor to be contained in the boundary. In addition, we study a bifurcation which takes place in the boundary of the non-negative orthant of the n-dimensional Euclidean space.

Keywords

Fixed point Dissipative flow Global attractor Index Bifurcation 

Mathematics Subject Classification

34D23 54H20 37G35 37C25 34D10 37C70 37B30 

Notes

Acknowledgements

The authors would like to express their gratitude to the referees for their useful suggestions which have helped to improve the manuscript.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Escuela Técnica Superior de Ingenieros InformáticosUniversidad Politécnica de MadridMadridSpain
  2. 2.Facultad de C.C. MatemáticasUniversidad Complutense de MadridMadridSpain

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