Emergence of local synchronization in neuronal networks with adaptive couplings

Chakravartula, Shilpa; Indic, Premananda; Sundaram, Bala; Killingback, Timothy

doi:10.1371/journal.pone.0178975

Cited by 28 publications

(17 citation statements)

References 67 publications

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“…Moreover, the findings on multicluster solutions as they are reported in this work are in very good agreement with previous results on adaptive neural networks [POP15,CHA17a]. Here, stable multicluster states of coherently spiking neurons with weak but time-dependent inter-cluster coupling were reported.…”

Section: Conclusion and Outlook9supporting

confidence: 92%

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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Section: Conclusion and Outlook9supporting

confidence: 92%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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“…In future work, it would be interesting to combine this model of gap junction short-term plasticity with our model. Chakravartula et al [ 88 ] introduced a new type of adaptive diffusive coupling in a network of Hindmarsh-Rose neurons [ 89 , 90 ]. They assumed that connections between pairs of neurons would follow a Hebb’s law [ 91 ], where neurons with simultaneous activity would strengthen their connection, while others with dissimilar activity would weaken their coupling.…”

Section: Discussionmentioning

confidence: 99%

Gap junction plasticity as a mechanism to regulate network-wide oscillations

2018

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Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap junction coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be modified in an activity-dependent manner, similar to chemical synapses. We hypothesized that activity-dependent gap junction plasticity acts as a mechanism to regulate oscillations in the cortex. We developed a computational model of gap junction plasticity in a recurrent cortical network based on recent experimental findings. We showed that gap junction plasticity can serve as a homeostatic mechanism for oscillations by maintaining a tight balance between two network states: asynchronous irregular activity and synchronized oscillations. This homeostatic mechanism allows for robust communication between neuronal assemblies through two different mechanisms: transient oscillations and frequency modulation. This implies a direct functional role for gap junction plasticity in information transmission in cortex.

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“…Such a structure leads to significantly different frequencies of the clusters and, as a result, to their uncoupling. This phenomenon is also reported for adaptive networks of Morris-Lecar, Hindmarsh-Rose, and Hodgkin-Huxley neurons with either spike-timing-dependent plasticity or Hebbian learning rule [39][40][41]. The role of hierarchy and modularity in brain networks has recently been discussed for real brain networks as well [42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 57%

Solitary states in adaptive nonlocal oscillator networks

Berner

Polanska

Schöll

et al. 2020

Eur. Phys. J. Spec. Top.

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In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling structure and the wavenumber which is a remarkable difference to an all-to-all coupled network. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states emerge due to the adaptive feature of the network and classify several bifurcation scenarios in which these states are created and stabilized.

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Emergence of local synchronization in neuronal networks with adaptive couplings

Cited by 28 publications

References 67 publications

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Gap junction plasticity as a mechanism to regulate network-wide oscillations

Solitary states in adaptive nonlocal oscillator networks

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