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.
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April 2021
Research Article|
April 26 2021
Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling
I. A. Shepelev
;
I. A. Shepelev
a)
1
Institute of Physics, Saratov State University
, 83 Astrakhanskaya Street, Saratov 410012, Russia
a)Author to whom correspondence should be addressed: igor_sar@li.ru
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S. S. Muni;
S. S. Muni
b)
2
School of Fundamental Sciences, Massey University
, Palmerston North, New Zealand
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T. E. Vadivasova
T. E. Vadivasova
c)
1
Institute of Physics, Saratov State University
, 83 Astrakhanskaya Street, Saratov 410012, Russia
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a)Author to whom correspondence should be addressed: igor_sar@li.ru
b)
Electronic mail: s.muni@massey.ac.nz
c)
Electronic mail: vadivasovate@yandex.ru
Note: This paper is part of the Focus Issue, In Memory of Vadim S. Anishchenko: Statistical Physics and Nonlinear Dynamics of Complex Systems.
Chaos 31, 043136 (2021)
Article history
Received:
February 22 2021
Accepted:
April 07 2021
Citation
I. A. Shepelev, S. S. Muni, T. E. Vadivasova; Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling. Chaos 1 April 2021; 31 (4): 043136. https://doi.org/10.1063/5.0048324
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