# 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

# gst: self-organized chimera states in pulse-coupled oscillator systems.

<< Coupled oscillator systems can lead to states in which synchrony and chaos coexist. These states are called “chimera states.” >>

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AA << study a variation of a pulse-coupled oscillator (PCO) model that has been shown to produce chimera states, demonstrate that it reproduces several of the expected chimera properties, like the formation of multiple heads and the ability to control the natural drift that Kuramoto's chimera states experience in a ring, and explain how chimera states emerge. >>️

<< Three notable aspects of chimeras in our PCO networks (with time-discrete coupling) are the absence of firing events from the tail (which still almost synchronize their phases), the reliable onset of the phenomenon from virtually any initial configuration, and the lack of a superimposed structure (e.g., artificially splitting the population into subgroups) and thus the self-organized nature of the phenomenon. >>️

Arke Vogell, Udo Schilcher, et al. Chimera states in pulse-coupled oscillator systems. Phys. Rev. E 110, 054214. Nov 26, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.054214 

Also: chimera, self-assembly, chaos, network,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, self-assembly, chaos, network 

# 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. >>

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<<  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: 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

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

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

# gst: apropos of transitions, towards a theory for the formation of chimera patterns in complex networks

This AA work << formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks. >>

They << show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. (AA) findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. >>

Malbor Asllani, Alex Arenas. Towards a Theory for the Formation of Chimera Patterns in Complex Networks. arXiv: 2412.05504v1 [nlin.AO]. Dec 7, 2024.

https://arxiv.org/abs/2412.05504

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

Keywords: gst, chimera, network, transition

# 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: self-organized target wave chimeras from asynchronous oscillators in reaction-diffusion media

<< An important development in nonlinear dynamics is the discovery of chimera states that represent the coexistence of synchronized and desynchronized activity in populations of identically coupled oscillators. >>

 Here, AA << unveil a novel chimera state called “self-organized target wave chimera” in reaction-diffusion media where synchronized target waves spontaneously emerge from a pacemaker composed of asynchronous oscillators. This regime contrasts with a widely accepted perspective that synchronized target waves can be generated only by the individuals, which comprise the pacemaker, behaving in a synchronized manner. >>

AA << characterize the features of self-organized target wave chimeras and present a phase diagram of existence of such a regime. >>

Bing-Wei Li, Jie Xiao, et al. Self-Organized Target Wave Chimeras in Reaction-Diffusion Media. Phys. Rev. Lett. 133, 207203. Nov 15, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.207203

Also: chimera, self-assembly, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, self-assembly, waves, self-organized target wave chimera, asynchronous oscillators

# 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: apropos of transverse instabilities, from chimeras to extensive chaos

<< Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can thus expect complex dynamics to arise in networks of such populations. >>️

Here AA << analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators, and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. >>️

Pol Floriach, Jordi Garcia-Ojalvo, Pau Clusella. From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations. arXiv: 2407.20408v2 [nlin.CD]. Oct 11, 2024.

https://arxiv.org/abs/2407.20408

Also: chimera, instability, chaos, network, in 

https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, instability, chaos, network

# 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

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

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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: 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. >>

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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: labyrinth chaos: revisiting the elegant, chaotic and hyperchaotic walks

<< Labyrinth chaos was discovered by Otto Rossler and Rene' Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, (AA) celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. >>

 << As all Rossler’s pioneering contributions, labyrinth chaos still holds promise for very interesting further developments. Its simplicity and elegance, both in terms of symmetries, topology and feedback-circuit structure, makes it a good candidate to compare it with other nonlinear, cyclically coupled systems, such as the Arabesques, the Lotka-Voltera system and its variants, and the Arnold-Beltrami-Childress  model. >> 

Vasileios Basios, Chris G. Antonopoulos, Anouchah Latifi. Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks. arXiv: 2011.11009v1. Nov 22, 2020.

https://arxiv.org/abs/2011.11009

# life: apropos of fuzzy cooperation, Ralph fuzzy mixture vs. world fuzzy dance ...

<< In 2013, the American virologist Ralph Baric approached Zhengli Shi at a meeting. Baric was a top expert in coronaviruses, with hundreds of papers to his credit, and Shi, along with her team at the Wuhan Institute of Virology, had been discovering them by the fistful in bat caves. In one sample of bat guano, Shi had detected the genome of a new virus, called SHC014, that was one of the two closest relatives to the original SARS virus, but her team had not been able to culture it in the lab. >>️

<< Baric had developed a way around that problem—a technique for “reverse genetics” in coronaviruses. Not only did it allow him to bring an actual virus to life from its genetic code, but he could mix and match parts of multiple viruses. He wanted to take the “spike” gene from SHC014 and move it into a genetic copy of the SARS virus he already had in his lab. The spike molecule is what lets a coronavirus open a cell and get inside it. The resulting chimera would demonstrate whether the spike of SHC014 would attach to human cells. >>️

<< Just as when you trade in part of a poker hand for fresh cards, there was no way of knowing whether the final chimeras would be stronger or weaker. >>

<< If you study a hundred different bat viruses, your luck may run out. >> Ralph Baric. 

<< In 2014, the NIH awarded a five-year, $3.75 million grant to EcoHealth Alliance to study the risk that more bat-borne coronaviruses would emerge in China, using the same kind of techniques Baric had pioneered. Some of that work was to be subcontracted to the Wuhan Institute of Virology. >>

<< Consider this hypothetical scenario, (..) An important gain-of-function experiment involving a virus with serious pandemic potential is performed in a well-regulated, world-class laboratory by experienced investigators, but the information from the experiment is then used by another scientist who does not have the same training and facilities and is not subject to the same regulations. In an unlikely but conceivable turn of events, what if that scientist becomes infected with the virus, which leads to an outbreak and ultimately triggers a pandemic >>  Anthony Fauci (director of the NIH’s National Institute of Allergy and Infectious Diseases) (2012).

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<< Paul’s grilling of Fauci brought new scrutiny to the relationship between Ralph Baric’s lab at UNC and Zhengli Shi’s at WIV, with some narratives painting Baric as the Sith master of SARS and Shi as his ascendant apprentice. They did share resources—for example, Baric sent the transgenic mice with human lung receptors to Wuhan.  >>

️

<< During a hearing on May 11, 2021, Senator Rand Paul confronted Anthony Fauci over funding of bat-virus research by the National Institutes of Health. >>️

<< The NIH has still not fully explained its decision-making and did not reply to questions. Citing a pending investigation, it has declined to release copies of the grant that sent the Wuhan institute about $600,000 between 2014 and 2019. It has also revealed little about its new system for assessing gain-of-function risks, which is carried out by an anonymous review panel whose deliberations are not made public. >>️

️

Rowan Jacobsen. Inside the risky bat-virus engineering that links America to Wuhan. China emulated US techniques to construct novel coronaviruses in unsafe conditions. MIT TechRev. Jun 29, 2021. 

https://www.technologyreview.com/2021/06/29/1027290/gain-of-function-risky-bat-virus-engineering-links-america-to-wuhan

Also

<< " ... e Da-Li' si sparse pell' aere un fantasmatico ente supersintetico supercompresso ... >> in: ️2153 - cracker tendenziali (around a matter-sucking maelstrom). Notes. Apr 4, 2008. (quasi-stochastic poetry)

https://inkpi.blogspot.com/2008/04/cracker-tendenziali-around-matter.html

<< in attesa del beffardo tsunami. >> in: 1619 - onda di carambola. Notes. Nov 29, 2004. (quasi-stochastic poetry).

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https://inkpi.blogspot.com/2004/11/1619-onda-di-carambola.html

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

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FonT

no surprise, no amazement here, I know chickens behaviors. 

<< Ricordo che quando si era ragazzi, negli anni sessanta, ... >> in: 2157 - il pino di takata matsubara. Apr 1, 2011. Notes. 

https://inkpi.blogspot.com/2011/04/2157-il-pino-di-takata-matsubara.html