Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling
I.A. Shepelev, Saratov State University, Russia; T.E. Vadivasova, Saratov State University, Russia
Abstract
We study the dynamics of a 2D lattice of the van der Pol oscillators, which are coupled by the nonlocal nonlinear repulsive coupling. The type of coupling under exploration can be organized by using nonlinear active elements having a negative resistance region in their current-voltage characteristic curve (for example, a tunnel diode). The coupling can be divided into two components, namely the linear repulsive and the nonlinear attractive coupling. The important feature in the dynamics of the lattice with the repulsive coupling is the absence of any type of propagating wave regimes. There are only standing waves with periodic temporal behavior and different spatiotemporal structures. We explore the features of the formation of the simple and complex spatiotemporal patterns in the lattice when the coupling parameters are varied. We show that the presence of the repulsive coupling term leads to the emergence of a lot of new periodic states of individual oscillators, while the attractive nonlinear coupling term attenuates this effect. The regime diagram in the parameter plane (coupling range-coupling strength) is numerically obtained. We also show the role of the coupling nonlinearity in the formation of different spatiotemporal dynamics in the lattice.
Speaker
Shepelev Igor A.
Saratov State University
Russia
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