# gst: apropos of transitions, rich behaviors from chimeras or solitary states to traveling waves

AA << study numerically the spatiotemporal dynamics of a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. >>

<< It is shown that the discretized oscillator exhibits a richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Such regimes as the coexistence of multichimera state/traveling wave and solitary state are revealed for the first time and studied in detail. >>

<< It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient towards the purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, observation time, initial conditions, and influence of external noise. >>

Elena Rybalova, Sishu Muni, Galina Strelkova. Transition from chimera/solitary states to traveling waves. arXiv: 2212.07990v1 [nlin.AO]. Dec 15, 2022. 

https://arxiv.org/abs/2212.07990

Also

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni

keyword 'waves' in FonT

https://flashontrack.blogspot.com/search?q=waves

keyword 'onda' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=onda

Keywords: gst, behavior, van der Pol oscillator, transition, chimera state, solitons, solitary state, waves, noise

# gst: the solitary route to chimera states.

AA << show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit (they) demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. (AA) demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators. >>

<<  While it is well known that self-organized wave patterns typically coexist within an interval of possible different wave numbers (..)(AA) show here the coexistence of coherence-incoherence patterns with different numbers of incoherent oscillators, which are in fact coexisting chaotic attractors with different Lyapunov dimensions. The incoherent oscillators in these coexisting attractors show extensive chaos of different dimensions. The total share of incoherent oscillators in a chimera state is a macroscopic quantity. Hence, within the range of such shares, where stable chimera states exist, (AA) find, for large systems, an increasing number of coexisting attractors with their numbers of incoherent oscillators increasing as well. (They) showed that, varying the coupling parameter, this extensive scenario is linked to the thermodynamic limit of the solitary regime, where the range of admissible numbers of incoherent oscillators shrinks down to one single oscillator in an infinitely large system. For this case, the emergence of the chaotic motion of the single incoherent oscillator could be shown in a period doubling cascade. >>

Leonhard Schulen, Alexander Gerdes, et al. The solitary route to chimera states. arXiv:2204.00385v1 [nlin.CD]. Apr 1, 2022.

https://arxiv.org/abs/2204.00385

Also

keyword 'FitzHugh-Nagumo oscillators' in APS | PubMed

https://journals.aps.org/search/

https://pubmed.ncbi.nlm.nih.gov/?term=FitzHugh-Nagumo+oscillators

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, solitons, solitary states, period-doubling cascade, chaos, Lyapunov dimension, FitzHugh-Nagumo oscillator, chimera state, dynamical systems.