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Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory
(Journal of Differential Equations, 2017-12-15) [Artigo]
We study the regularization of an oriented 1-foliation F on M∖Σ where M is a smooth manifold and Σ⊂M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define ...
Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation
(Journal of Mathematical Physics, 2011-11-01) [Artigo]
In this paper we study the fourth order differential equation d(4)u/dt(4) + q d(2)u/dt(2) + u(3) - u = 0, which arises from the study of stationary solutions of the Extended Fisher-Kolmogorov equation. Denoting x = u, y = ...
Synchronization and Non-Smooth Dynamical Systems
(Journal of Dynamics and Differential Equations, 2012-03-01) [Artigo]
In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. ...