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AuthorFrantzeskakis D.J.
AuthorKarachalios N.I.
AuthorKevrekidis P.G.
AuthorKoukouloyannis V.
AuthorVetas K.
Available date2020-04-09T12:27:31Z
Publication Date2019
Publication NameJournal of Mathematical Analysis and Applications
ResourceScopus
ISSN0022247X
URIhttp://dx.doi.org/10.1016/j.jmaa.2018.11.039
URIhttp://hdl.handle.net/10576/14059
AbstractWe consider the energy landscape of a dissipative Klein–Gordon lattice with a on-site potential. Our analysis is based on suitable energy arguments, combined with a discrete version of the Łojasiewicz inequality, in order to justify the convergence to a single, nontrivial equilibrium for all initial configurations of the lattice. Then, global bifurcation theory is explored, to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states. Direct numerical simulations reveal the rich structure of the equilibrium set, consisting of non-trivial topological (kink-shaped) interpolations between the adjacent minima of the on-site potential, and the wealth of dynamical convergence possibilities. These dynamical evolution results also provide insight on the potential stability of the equilibrium branches, and glimpses of the emerging global bifurcation structure, elucidating the role of the interplay between discreteness, nonlinearity and dissipation.
Sponsorsupported by NPRP grant # [ 9-329-1-067 ] from Qatar National Research Fund (a member of Qatar Foundation). The findings achieved herein are solely the responsibility of the authors. The authors D.J.F. and P.G.K. gratefully acknowledge the support of the Greek Diaspora Fellowship Program of Stavros Niarchos Foundation .
Languageen
PublisherAcademic Press Inc.
SubjectBifurcations of equlilibria
Discrete Klein�Gordon equation
Dissipation
Limit set
Nonlinear lattices
Lojasiewicz inequality
TitleDynamical transitions between equilibria in a dissipative Klein-Gordon lattice
TypeArticle
Pagination546-576
Issue Number1
Volume Number472
dc.accessType Abstract Only


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