Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
KeywordsDynamical system, nonlinear semigroup, attractor, gradient-like semigroup, Łojasiewicz-Simon inequality
AbstractWe consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from $-\infty $ and goes to $\infty $ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Łojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.
How to Cite
ARAGÃO-COSTA, Eder R., CARVALHO, Alexandre N., MARÍN-RUBIO, Pedro & PLANAS, Gabriela. Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems. Topological Methods in Nonlinear Analysis [online]. 22 April 2013, T. 42, nr 2, s. 345–376. [accessed 30.1.2023].
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