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This article is cited in 1 scientific paper (total in 1 paper)
Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators
Vyacheslav P. Kruglovabc, Sergey P. Kuznetsovcb a Steklov Mathematical Institute, Russian Academy of Sciences,
ul. Gubkina 8, Moscow, 119991 Russia
b Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch,
ul. Zelenaya 38, Saratov, 410019 Russia
c Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
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.
Keywords:
reversibility, involution, Hamiltonian system, Topaj – Pikovsky model, phase oscillator lattice.
Received: 28.10.2019 Accepted: 11.11.2019
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
Linking options:
https://www.mathnet.ru/eng/rcd1036 https://www.mathnet.ru/eng/rcd/v24/i6/p725
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