Dynamical transitions between equilibria in a dissipative Klein-Gordon lattice

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Frantzeskakis, D. J.¹  Karachalios, N. I.²  Kevrekidis, P. G.³  Koukouloyannis, V.⁴  Vetas, K.² 

[1] Univ Athens, Dept Phys, Athens 15784, Greece

[2] Univ Aegean, Dept Math, Karlovassi 83200, Samos, Greece

[3] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[4] Qatar Univ, Coll Arts & Sci, Dept Math Stat & Phys, POB 2713, Doha, Qatar

关键词: Nonlinear lattices;    Discrete Klein-Gordon equation;    Dissipation;    Limit set;    Bifurcations of equlilibria;    Lojasiewicz inequality;   

DOI  :  10.1016/j.jmaa.2018.11.039

来源: Elsevier

【 摘 要 】

We consider the energy landscape of a dissipative Klein-Gordon lattice with a phi(4) on-site potential. Our analysis is based on suitable energy arguments, combined with a discrete version of the Lojasiewicz 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free