Abstract:
We discuss the Hamiltonian model of an oscillator lattice with local coupling. The Hamiltonian model describes localized spatial modes of nonlinear the Schrödinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of the Topaj – Pikovsky phase oscillator lattice. Furthermore, the Hamiltonian system has invariant manifolds with asymptotic dynamics exactly equivalent to the Topaj – Pikovsky model. We examine the stability of trajectories belonging to invariant manifolds by means of numerical evaluation of Lyapunov exponents. We show that there is no contradiction between asymptotic dynamics on invariant manifolds and conservation of phase volume of the Hamiltonian system. We demonstrate the complexity of dynamics with results of numerical simulations.
The work of V. P.Kruglov and S.P.Kuznetsov was supported by the grant of the Russian
Science Foundation (project no. 15-12-20035) (formulation of the problem, analytical calculations
and research of related topics (Sections 1 and 2)). The work of V. P.Kruglov was supported by
the grant of the Russian Science Foundation (project no. 19-71-30012) (analytical and numerical
calculations and interpretation of obtained results (Sections 3–6)).
Citation:
Vyacheslav P. Kruglov, Sergey P. Kuznetsov, “Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 725–738
\Bibitem{KruKuz19}
\by Vyacheslav P. Kruglov, Sergey P. Kuznetsov
\paper Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 725--738
\mathnet{http://mi.mathnet.ru/rcd1036}
\crossref{https://doi.org/10.1134/S1560354719060108}
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This publication is cited in the following 1 articles:
I. Bashkirtseva, L. Ryashko, “Chaotic transients, riddled basins, and stochastic transitions in coupled periodic logistic maps”, Chaos, 31:5 (2021), 053101
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