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

Abstract

The behaviour of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimeralike regimes are observed at small values of the coupling strength parameter. Synchronization takes place with increasing of the coupling strength and coupling range parameters. Various chimera and solitary states are realised when the coupling strength parameter is sufficiently large. The single van der Pol oscillator is taken in the regime of relaxation oscillations. Therefore, the lattice may realise spiral wave and spiral wave chimera regimes. Besides, target wave and solitary state regimes are observed in the ensemble. Finally, the solitary state and solitary state chimera regimes are firstly shown for the lattice of coupled van der Pol oscillators.

Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling

“…It is clearly seen that the oscillations correspond to different limit cycles. This feature of the oscillators of incoherence domain is similar with the feature of solitary states, which are observed in different systems with attractive coupling [17,23,44,42,35,40], including the lattice of van der Pol oscillators [41]. Thus, this regime can be considered as a type of solitary state.…”

“…Moreover, the coefficient of nonlinear coupling does not depend on values of coupling strength σ of linear coupling and of the coupling range P . This character of coupling extremely changes the dynamics of the system and the dynamical regimes becomes completely different from the case of a 2D lattice of van der Pol oscillators with common attractive (dissipative) coupling [9,41]. For example, all the regimes represent standing waves for any randomly distributed initial conditions under consideration.…”

“…Hence, when the nonlinear attractive coupling term prevails over the linear one, the system under study becomes two-state with two distinctive stable periodic attractors in the phase plane of individual oscillators. Thus, the chimera states in the lattice ( 7) are similar to solitary state chimeras, which exist in a lattice of van der Pol oscillators with the attractive coupling [41] and other systems [37,34,25].…”

Detecting spiral wave tips using deep learning

“…Tracking spiral wave tips is relevant, for example, in the context of controlling 4 – 6 , and investigating the structure and governing processes during spiral wave chaos 7 , 8 , analyzing the complexity during cardiac arrhtyhmias 9 , 10 , or studying creation/termination mechanisms which may also lead to self-termination 11 – 13 . Spiral or scroll waves can also be found and studied in 3D chemical reactions (scroll waves), like the Belousov–Zhabotinsky reaction 14 , in arrays of non-linear Chua’s circuits 15 or 2D lattices of van der Pol oscillators 16 .…”

Synchronization scenarios in three-layer networks with a hub

“…The surprising aspect of this phenomenon is that these states were detected in systems of identical oscillators coupled in a symmetric ring topology with a symmetric interaction function, and they coexist with a stable completely synchronized state. The last a) Electronic mail: zergon@gmx.net decade has seen an increasing interest in phase and amplitude chimeras both in time-continuous systems [14][15][16][17][18][19][20][21][22] and in timediscrete maps [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] . It has been shown that they are not limited to phase oscillators, but can be found for a large variety of different dynamics including neural systems [42][43][44][45][46][47][48] .…”