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- W2950572227 abstract "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 L{}ojasiewicz 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." @default.
- W2950572227 created "2019-06-27" @default.
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- W2950572227 date "2018-09-21" @default.
- W2950572227 modified "2023-09-27" @default.
- W2950572227 title "Dynamical transitions between equilibria in a dissipative Klein-Gordon lattice" @default.
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- W2950572227 doi "https://doi.org/10.48550/arxiv.1809.07995" @default.
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