# gst: near the Hopf boundary, Intermittency and chimera states.

AA << study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. >>️

<< For analysis, (AA) first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. >>

<< Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks. >>️

Anjuman Ara Khatun, Yusra Ahmed Muthanna, et al. Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states. Phys. Rev. E 109, 034208. March 15, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034208

Also: transition, intermittency, chaos, chimera, network, in https://www.inkgmr.net/kwrds.html

Keywords: gst, transition, intermittency, chaos, chimera, network

# gst: emergence of chimeras driven by non-normality

<< The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. >>️

<< Particular attention has been paid to the emergence of chimera states, where subsets of synchronized oscillations coexist with asynchronous ones. Such coexistence of coherence and incoherence is a perfect example where order and disorder can persist in a long-lasting regime. >>

<< Based on a symmetry-breaking mechanism, in this paper, (AA) shed light on the role that non-normality, a ubiquitous structural property of real networks, has in the emergence of several diverse dynamical phenomena, e.g., amplitude chimeras or oscillon patterns. >>️

<< Specifically, (they) demonstrate that the prevalence of source or leader nodes in networks leads to the manifestation of phase chimera states. >>️

Riccardo Muolo, Joseph D. O'Brien, et al. Persistence of chimera states and the challenge for synchronization in real-world networks. arXiv: 2306.00237v1 [nlin.PS]. May 31, 2023.

https://arxiv.org/abs/2306.00237

Also: chimera, network, in: https://www.inkgmr.net/kwrds.html

Keywords: gst, chimera, network, synchronization, swarm, noise, order, disorder, normal

# gst: chimera resonance, in analogy with the effects of stochastic and coherence resonance

AA << explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. >>

️

<<  It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. >>

<< This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance. >>️

Elena Rybalova, Vasilii Nechaev, Eckehard Schöll, Galina Strelkova. Chimera resonance in networks of chaotic maps. arXiv:2307.00006v2 [cond-mat.dis-nn]. Jul 5, 2023.

https://arxiv.org/abs/2307.00006

Also: chimera, noise, chaos, network,  in: https://www.inkgmr.net/kwrds.html

Keywords: gst, chimera, noise, chaos, network, chimera resonance

# gst: sudden phase transitions among nonconservative system with nonreciprocal interactions

<< A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. >>️

Here AA reported << the emanation of a chimera in a network of Stuart-Landau oscillators. >>

<< The findings could have pragmatic implications in the areas of active matter, networks, and photonics. >>

️

M. Paul Asir. Emergence of chimeras: An impetus by exceptional points. Phys. Rev. E 108, 024220. Aug 22, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024220

Also: Stuart–Landau equation. 

https://en.m.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation

Also: network, transition, chimera, chaos, in: https://www.inkgmr.net/kwrds.html

Keywords: network, transition, chimera, chaos, pattern formation

# gst: apropos of coexistence of coherent and incoherent oscillators, chaotic chimera attractors in a triangular network.

<< A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. >>️

<< In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically. >>

<< In this paper, (AA) study the full phase space dynamics of such three-population networks. (They) demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. >>

<< The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold. >>️

Seungjae Lee, Katharina Krischer. Chaotic chimera attractors in a triangular network of identical oscillators. Phys. Rev. E 107, 054205. May 8, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054205

Also: chimera, chaos, three balls, in https://www.inkgmr.net/kwrds.html

Keywwords: gst, chimera, bifurcations, chaos, synchronization

# gst: even a tiny noise could self-induce new chimera patterns through stochastic resonance

<< Noise induced order in excitable systems has diverse manifestations, such as coherence resonance (CR) and stochastic resonance. In this context a less explored phenomenon is self-induced stochastic resonance (SISR). Unlike CR, SISR may arise away from the bifurcation threshold and the properties of the induced oscillations depend upon both the noise intensity and the time-scale separation factor. In this work, (AA) report a new chimera pattern in a network of coupled excitable units, namely the self-induced stochastic resonance chimera or SISR-chimera that originates from the SISR phenomenon. (AA) explore the detailed dynamics of the SISR-chimera in the parameter space using proper quantitative measures. (AA) have found that unlike CR chimera, the SISR-chimera pattern strongly depends upon the ratio of time scale and noise intensity. Therefore, this type of chimera pattern can be induced even for a tiny noise intensity if the time scale separation of the activator and inhibitor is large enough. >>️

Taniya Khatun, Tanmoy Banerjee. Genesis of chimera patterns through self-induced stochastic resonance. arXiv:2305.06824v1 [nlin.AO]. May 11, 2023. 

https://arxiv.org/abs/2305.06824

Also:  chimera, noise, disorder in  https://www.inkgmr.net/kwrds.html  

Keywords: gst, noise, disorder, chimera, self-induced stochastic resonance chimera 

# gst: emergence of the traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera in a two-dimensional network

<< Neuronal synchronization being a phenomenon linked to several brain pathologies such as epilepsy, Parkinson diseases, Alzheimer, autism and schizophrenia, does not always appear in a singular way in neuronal networks. Its presence (state of coherence) accompanied simultaneously by an asynchronous state (state of incoherence) has been demonstrated (..) in the networks of identical oscillators not locally coupled. This phenomenon was later termed the chimera state. (..) Chimera states are analogously to the cerebral behaviors of certain aquatic mammals and migratory birds, which during their movements half part of their brains asleep while the rest are awake.  >>️

AA << study the emergence of the traveling chimera state in a two-dimensional network of (..) burst neurons with the mutual presence of local and non-local couplings. (AA) show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. >>️

Gael R. Simo, Patrick Louodop, et al. Traveling chimera patterns in two-dimensional neuronal network. arXiv:2106.08400v1. Jun 9, 2021.

https://arxiv.org/abs/2106.08400