On a Smale Theorem and Nonhomogeneous Equilibria in Cooperative Systems

Simple item page
dc.creatorEnciso, German A.
dc.date2007-06-09
dc.date.accessioned2026-07-07T08:04:48Z
dc.date.available2026-07-07T08:04:48Z
dc.descriptionA standard result by Smale states that n dimensional strongly cooperative dynamical systems can have arbitrary dynamics when restricted to unordered invariant hyperspaces. In this paper this result is extended to the case when all solutions of the strongly cooperative system are bounded and converge towards one of only two equilibria outside of the hyperplane. An application is given in the context of strongly cooperative systems of reaction diffusion equations. It is shown that such a system can have a continuum of spatially inhomogeneous steady states, even when all solutions of the underlying reaction system converge to one of only three equilibria.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/0706.1331
dc.identifierhttp://arxiv.org/abs/0706.1331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130100
dc.subjectDynamical Systems
dc.subjectAnalysis of PDEs
dc.subject34C12, 35K57
dc.titleOn a Smale Theorem and Nonhomogeneous Equilibria in Cooperative Systems
dc.typetext

Files

Collections

arXiv