Localized solutions in lattice systems and their bifurcations caused by spatial interactions

Leonid A. Bunimovich, Dmitry Turaev

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We demonstrate the scenario showing how the stable spatially localized solutions with nontrivial (periodic, quasiperiodic or chaotic) dynamics may appear in lattice dynamical systems. It is important to mention that bifurcations to such regimes occur when the strength of spatial interactions exceeds some threshold. In fact we first prove the persistence of stationary localized structures in a range of weak interactions and then from this result of the 'anti-integrable limit' type we make the next step to show the existence of bifurcations of these states to the stable spatially localized states with a nontrivial time dynamics. We also show how our approach can be applied to sludy bifurcations to nonstationary states with spatial structure of general type.

Original languageEnglish
Pages (from-to)1539-1545
Number of pages7
JournalNonlinearity
Volume11
Issue number6
DOIs
StatePublished - 1 Nov 1998
Externally publishedYes

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