Clustering in delay-coupled smooth and relaxational chemical oscillators

Blaha, Karen; Lehnert, Judith; Keane, Andrew; Dahms, Thomas; Hövel, Philipp; Schöll, Eckehard; Hudson, John L.

doi:10.1103/physreve.88.062915

Cited by 26 publications

(37 citation statements)

References 25 publications

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“…This chapter closely mirrors our recently accepted paper with Eckehard Schöll's group [69]. Here, we select sets of four oscillators from the whole population of 64; we apply time-delayed coupling to induce phase locking.…”

Section: Notes To the Readermentioning

confidence: 97%

“…Ref. [69] demonstrated that, given knowledge of the interaction function, we can accurately predict clustering on networks of such oscillators. In principle, we are able to engineer the radial interaction function now that we have connected stimulation and behavior.…”

Section: Discussionmentioning

confidence: 99%

“…[69] for coupled higher-harmonic oscillators. This method can apply to any topology, but we focus on the unidirectional ring, which we employ in Sec.…”

Section: Theorymentioning

confidence: 99%

“…We present a short summary of relevant results from Ref. [69] in Section 6.4 and introduce the two-variable model. We discuss two experimental results in Section 6.5.…”

Section: Introductionmentioning

confidence: 99%

“…A recent study [69] investigated the clustering of delay-coupled rings of oscillators described by the observable variables of phase and radius (amplitude). The study used experimental oscillators in two regimes: (1) shown previously [33,87] in phase-only models such as the Kuramoto phase oscillator model [8].…”

Section: Introductionmentioning

confidence: 99%

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Improving Reduced Variable Models for Complex Systems via Experiment

Blaha

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Populations of simple interacting oscillators can give rise to complex dynamics.Real-world examples of such systems abound in biology, chemistry, and physics.Reduced-variable models can describe these systems. The phase model is a particularly successful reduced-variable model which, in its simplest form, each element is represented by one variable, the phase of oscillation. The phase model can be constructed from observable variables, without specific knowledge of underlying phenomenological behavior. Such reduced variable models are easier to construct and more generalizable than models derived from underlying physics or chemistry.In this dissertation, we study the dynamics of a population of coupled electrochemical oscillators in order to modify the phase model to expand its applicability.Specifically, we develop a two-phase model, a phase and radius model, and models with network coupling.We analyze data from two coupled oscillators with a standard one-dimensional phase model and a newer two-dimensional phase model. The same quantity of data is needed for either model. The two-dimensional analysis reveals behaviors and coupling parameters in theoretical and experimental examples that the onedimensional analysis does not show. The two-dimensional model could be useful in systems that exhibit learning due to its ability to distinguish stimulation and reaction. We extend the Stuart-Landau model to describe clustering dynamics for higher harmonic oscillators. We present examples of asymmetrical clusters arising from networks of higher harmonic oscillators. We show that the amplitude of oscillation is functionally influenced by coupling; we believe this "amplitude coupling function" has not been previously described. This function can be constructed from the original time series with no additional measurements.Recently, combined phase and amplitude models have gained attention; we explore the conditions where a phase and amplitude model is useful. We show experimentally a change in cluster state due only to changes in coupling strength. Such a transition is not possible with a phase-only model. Simulations with the extended Stuart-Landau model match experimental results. We demonstrate a method for predicting the amplitude coupling function from the coupling. Prior to this study, the relationship between stimulation and response was not known for the amplitude. We suggest that the phase and amplitude model will be most useful (1) in modeling high-harmonic oscillations, and (2) where coupling exceeds the "weak coupling" approximation of the phase-only model. iv

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Section: Notes To the Readermentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

“…[69] for coupled higher-harmonic oscillators. This method can apply to any topology, but we focus on the unidirectional ring, which we employ in Sec.…”

Section: Theorymentioning

confidence: 99%

“…We present a short summary of relevant results from Ref. [69] in Section 6.4 and introduce the two-variable model. We discuss two experimental results in Section 6.5.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improving Reduced Variable Models for Complex Systems via Experiment

Blaha

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Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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Collective phenomena in systems of interconnected dynamical units are omnipresent in nature. The swarm behavior in flocks of birds or schools of fish, the synchronous flashing of fireflies or even coherent spiking of neurons in the human brain are just a few examples of collective motion. Elucidating the mechanisms that give rise to synchronization is crucial in order to understand biological self-organization. For this sake, the theory of dynamical networks has been successfully applied over the last decades to boil down the complex dynamics from natural systems to their essentials. In addition, dynamical networks with adaptive couplings and hence non-constant network structure appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. In this thesis, we study adaptive networks and their properties which give rise to the emergence of a variety of synchronization patterns, including complete and cluster synchronization as well as solitary and chimera-like states. One of the main fields of application that is investigated in this thesis concerns neuroscience. However, the methods and approaches developed in this work are not restricted to a specific field of application.aus gekoppelten Phasenoszillatoren an und zeigen, wie das subtile Zusammenspiel zwischen Adaptivität und Netzwerkstruktur die Entstehung komplexer partieller Synchronisationsmuster hervorruft.Trotz des regen Interesses an adaptiven Netzwerken ist über das Zusammenspiel adaptiv gekoppelter Netzwerkgruppen wenig bekannt. Solche adaptiven Mehrschicht-oder Multiplex-Netzwerke kommen in neuronalen Netzwerken ganz natürlich vor. Wir schlagen ein Konzept zur Erzeugung und Stabilisierung diverser partieller Synchronisationsmuster (Phasen-Cluster) in adaptiven Netzwerken vor. Wir zeigen, dass das "Multiplexen" verschiedene stabile Phasen-Cluster-Zustände induzieren kann, selbst wenn diese in den Einschicht-Systemen nicht stabil sind oder gar nicht existieren. Weiterhin entwickeln wir eine Methode zur Analyse von Laplace-Matrizen von Multiplex-Netzwerken, die einen Einblick in die spektrale Struktur dieser Netzwerke ermöglicht und damit eine Reduktion des Stabilitätsproblems auf die von Einschicht-Netzwerken ermöglicht. Wir setzen die neue Methode ein, um analytische Ergebnisse für die Stabilität der Zustände im Mehrschicht-System zu erhalten.

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One-Cluster States in Adaptive Networks of Coupled Phase Oscillators

Berner

2021

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

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Clustering in delay-coupled smooth and relaxational chemical oscillators

Cited by 26 publications

References 25 publications

Improving Reduced Variable Models for Complex Systems via Experiment

Improving Reduced Variable Models for Complex Systems via Experiment

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

One-Cluster States in Adaptive Networks of Coupled Phase Oscillators

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