Stable amplitude chimera in a network of coupled Stuart-Landau oscillators

Sathiyadevi, K.; Chandrasekar, V. K.; Senthilkumar, D. V.

doi:10.1103/physreve.98.032301

Cited by 38 publications

(16 citation statements)

References 47 publications

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“…Diverse collective states in the form of cluster chimera death and solitary state are observed in nonlocally coupled oscillatory systems with attractive and repulsive couplings [59]. Stable amplitude chimera and traveling wave states are encountered in nonlocally coupled network of oscillators in presence of both attractive and repulsive interactions [60]. In the following, we discuss about a significant observation of frequency-modulated chimera-like pattern during explosive transitions to synchronization in networks of the heterogeneous Kuramoto model [61].…”

Section: (4)mentioning

confidence: 96%

Perspective on attractive-repulsive interactions in dynamical networks: Progress and future

Majhi

Chowdhury

Ghosh

2020

EPL

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PACS 05.45.Xt -Coupled oscillators PACS 05.90.+m -Nonlinear dynamical systems PACS 89.75.-k -Complex systems PACS 89.75.Fb -Structures and organization in complex systemsAbstract. -Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the synergy of attractive and repulsive interactions influence the destiny of ensembles of interacting dynamical systems. We review the incarnation of collective states ranging from chimera or solitary states to extreme events and oscillation quenching arising as a result of different network arrangements. Though the existing literature demonstrates that many of the crucial developments have been made, nonetheless, we come up with significant routes of further research in this field of study.

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Section: (4)mentioning

confidence: 96%

Perspective on attractive-repulsive interactions in dynamical networks: Progress and future

Majhi

Chowdhury

Ghosh

2020

EPL

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“…We choose the same parameter configuration as in [45]: w = = = N P 2, 100, 1 N 1 and = P 22 2 . In our experiments we vary = K r P N ,…”

Section: Parameter Configurationmentioning

confidence: 99%

Monte Carlo basin bifurcation analysis

2020

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Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds-Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart-Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language.world applications: the Dodds-Watts model of social and biological contagion, a network of second order Kuramoto oscillators, used e.g. to model power grids and a network of Stuart-Landau oscillators, of importance for many chemical and biological systems, will follow in section 3. Lastly, these results and the performance and applicability of the presented method will be discussed in section 4.

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“…Depending on the attributes of the spatiotemporal distribution of the constituting elements associated with a system of interacting identical dynamical units, chimera states are categorized as amplitude chimera [52][53][54][55], traveling chimera [56][57][58], globally clustered chimera [59], breathing chimera [60][61][62], etc. In this regard, exploration on the emergence of amplitude mediated chimera state by Sethia et al [63,64] is noteworthy.…”

Section: Introductionmentioning

confidence: 99%

Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

Kundu,

Muruganandam,

Ghosh

et al. 2021

Preprint

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Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.

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Stable amplitude chimera in a network of coupled Stuart-Landau oscillators

Cited by 38 publications

References 47 publications

Perspective on attractive-repulsive interactions in dynamical networks: Progress and future

Perspective on attractive-repulsive interactions in dynamical networks: Progress and future

Monte Carlo basin bifurcation analysis

Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

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