Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

• Published in: Chaos, solitons and fractals Vol. 135; p. 109725
• Main Authors: Shepelev, I.A., Bukh, A.V., Muni, S.S., Anishchenko, V.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2020
• Subjects: Chimera state; Nonlocal coupling; Solitary state; Solitary state chimera; Spatiotemporal pattern formation; Spiral wave; Spiral wave chimera; Target wave; Target wave chimera; van der Pol oscillator; Spatiotemporal pattern formation; van der Pol oscillator; Solitary state; Solitary state chimera; Nonlocal coupling; Target wave chimera; Spiral wave; Target wave; Chimera state; Spiral wave chimera
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.109725

•General spatiotemporal patterns is studied for the varying coupling parameters.•A role of solitary states in forming spatiotemporal structures are discovered.•Solitary state chimera is firstly found in a network of continuous-time oscillators. We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures including chimera states when the coupling parameters are varied. Spiral wave chimeras are formed in the network when the coupling strength is rather large and the coupling range is short enough. Another type of chimeras is a target wave chimera. It is shown that solitary states play a crucial role in forming an incoherence cluster of this chimera state. They can also spread within the coherence cluster. Furthermore, when the coupling range increases, the target wave chimera evolves to the regime of solitary states which are randomly distributed in space. Growing the coupling strength leads to the attraction of solitary states to a certain spatial region, while the synchronous regime is set in the other part of the system. This spatiotemporal pattern represents a solitary state chimera, which is firstly found in the system of continuous-time oscillators. We offer the explanation of these phenomena and describe the evolution of the regimes in detail.