Geodesic
Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 82-94

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We consider a two-dimensional lattice of the coupled van der Pol oscillators obtained by the standard space discretization of a nonlinear wave equation $$ u_{tt}+\varepsilon(u^2-1)u_t+u=a_1^2u_{xx}+a_2^2u_{yy},\qquad a_1,a_2=\text{const}>0,\quad0\varepsilon\ll1, $$ in the unit square subject to the zero Neumann boundary conditions. We prove that the related system of ordinary differential equations owns attractors which have not analogues in the original boundary problem. They are stable invariant tori of different dimensions. It is shown that the number of this tori grows without limit as the number of equations in the lattice increases.
Keywords: lattice of connected oscillators, attractor, bufferness.
Mots-clés : invariant torus 
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     title = {Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators},
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A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 82-94. http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a10/