Geodesic
Autowave structures in two-dimensional lattices of nonlocally coupled oscillators
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 3, pp. 299-323.

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Objective. The aim of the research was to compare the dynamics of spiral and target structures including the dynamics of chimera states in ensembles with different nodes. Numeric simulations for autowave structures in two-dimensional ensembles of coupled van der Pol oscillators and Rulkov's maps were performed. Cases of local and nonlocal coupling between ensemble nodes were considered. Methods. The evolution dynamics of Rulkov's map lattice is strictly defined with corresponding recurrent formulae. The ensemble of van der Pol oscillators was integrated using the Heun's method. Snapshots of amplitude values, spatio-temporal diagrams for corresponding sections, phase portraits and time series for single elements were constructed. Moreover, mean values of frequencies of all nodes, and dependencies of instantaneous frequencies on time for selected maps and oscillators. Results were compared. Results. It is shown that classical spiral and target wave regimes were realized at local coupling. More complex structures including chimera states were obtained when a nonlocal coupling was included. Spiral wave chimera structures with single and several incoherent cores were described. A new chimera structure based on target waves (target wave chimera) was shown to be possible. The analysis of features of incoherent cores for both spiral wave chimera and target wave chimera were presented. The results of coupling parameter effect and external noise influence on the dynamics of the ensembles were discussed. Conclusion. Mean values of frequencies were almost the same for all the elements in both ensembles at target wave chimera regimes. The mean values in the incoherent core differed from the ones in coherent area at spiral wave chimera regimes. A transition from target waves to spiral waves was possible when a noise with sufficiently large intensity was introduced. Noise-induced transition from spiral waves to target waves took place in the ensemble of Rulkov's maps.
Keywords: two-dimensional ensemble, nonlocal coupling, spiral wave chimera, target wave chimera. 
@article{IVP_2020_28_3_a5,
     author = {A. V. Bukh and E. V. Rybalova and V. S. Anishchenko},
     title = {Autowave structures in two-dimensional lattices of nonlocally coupled oscillators},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {299--323},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2020_28_3_a5/}
}
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A. V. Bukh; E. V. Rybalova; V. S. Anishchenko. Autowave structures in two-dimensional lattices of nonlocally coupled oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 3, pp. 299-323. http://geodesic.mathdoc.fr/item/IVP_2020_28_3_a5/