Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling

We explore the emergence of a variety of different spatiotemporal patterns in a 2D lattice of self-sustained oscillators, which interact nonlocally through an active nonlinear element. A basic element is a van der Pol oscillator in a regime of relaxation oscillations. The active nonlinear coupling can be implemented by a radiophysical element with negative resistance in its current-voltage curve taking into account nonlinear characteristics (for example, a tunnel diode). We show that such coupling consists of two parts, namely, a repulsive linear term and an attractive nonlinear term. This interaction leads to the emergence of only standing waves with periodic dynamics in time and absence of any propagating wave processes. At the same time, many different spatiotemporal patterns occur when the coupling parameters are varied, namely, regular and complex cluster structures, such as chimera states. This effect is associated with the appearance of new periodic states of individual oscillators by the repulsive part of coupling, while the attractive term attenuates this effect. We also show influence of the coupling nonlinearity on the spatiotemporal dynamics.

Automated summary

In a 2D lattice of self-sustained oscillators interacting nonlocally through an active nonlinear element, various spatiotemporal patterns emerge, including standing waves with periodic dynamics and complex cluster structures such as chimera states. The variation of coupling parameters leads to different spatiotemporal patterns, with some new periodic states arising from the repulsive part of the coupling. The influence of coupling nonlinearity on spatiotemporal dynamics is also demonstrated.