Loss of synchronization in complex neuronal networks with delay

Lehnert, Judith; Dahms, Thomas; Hövel, Philipp; Schöll, Eckehard

doi:10.1209/0295-5075/96/60013

Cited by 60 publications

(64 citation statements)

References 36 publications

(27 reference statements)

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“…Time delays are always present in coupled systems due to the finite signal propagation time. These time lags give rise to complex dynamics and have been shown to play a key role in the synchronization behavior of systems [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], see also the review [43]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

Choe¹,

Kim²,

Jang³

et al. 2014

Int. J. Dynam. Control

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We suggest a delayed feedback control scheme with arbitrary delay for stabilizing a periodic orbit, while maintaining the noninvasiveness of the controller. Since the constraint on the delay to be adjusted to the period of the unstable periodic orbit is not imposed, a richer structure of the dynamics can be observed: Not only weakly unstable, but also strongly unstable periodic orbits are stabilized and even stabilization of orbits with infinite period is achieved. The control mechanism is elucidated for the generic model of a subcritical Hopf bifurcation. A complete bifurcation analysis for the fixed point as well as the periodic orbit is presented and the stability domains are identified. Furthermore, we study the effects of distributed delayed feedback on the stabilization of periodic orbits, and show that larger variance of the delay distribution considerably enlarges the stabilization region in the parameter space. We extend the control scheme to a network of Hopf normal forms coupled with heterogeneous delays. By tuning the coupling parameters, different synchronization patterns, i.e., in-phase, splay, and clustering, can be selected. The characteristic equation for Floquet exponents of the heterogeneous delay network is derived in an analytical form, which reveals the coupling parameters for successful stabilization. The equation takes a C.-U. Choe · R.-S. Kim · H. Jang Center for Nonlinear Science, University of Science, Unjong-District, Pyongyang, DPR Korea P. Hövel · E. Schöll (B) Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany e-mail: schoell@physik.tu-berlin.de P. Hövel Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany unified form for both subcritical and supercritical Hopf bifurcations regardless of the synchronization patterns. Analysis of Floquet exponents and direct numerical simulations show that the heterogeneity in the delays drastically facilitates stabilization and provides an enlarged parameter region for successful control. Finally, we consider the thermodynamic limit in the framework of a mean field approximation and show that heterogeneous delays offer an enhanced performance of control.

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Section: Introductionmentioning

confidence: 99%

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

Choe¹,

Kim²,

Jang³

et al. 2014

Int. J. Dynam. Control

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“…In [Lehnert, 2010;Lehnert et al, 2011a], it was shown that the MSF for all values of K and τ shows qualitatively the same behavior. In particular, the stable region is in very good approximation given by the unit cycle.…”

Section: Type-ii Excitabilitymentioning

confidence: 97%

“…In the last two decades dynamics on network received a growing amount of interest [Dhamala et al, 2004;Zigzag et al, 2009;Choe et al, 2010;Chavez et al, 2005;Sorrentino and Ott, 2007;Albert et al, 2000;Kinzel et al, 2009;Lehnert et al, 2011a;Keane et al, 2012]. One of the central topics of dynamics on networks is synchronization [Strogatz and Stewart, 1993;Rosenblum et al, 1996;Pikovsky et al, 2001;Pecora and Carroll, 1998;Mosekilde et al, 2002;Wang and Chen, 2002;Arenas et al, 2006aArenas et al, , 2008Balanov et al, 2009;Omelchenko et al, 2010;Schöll, 2013].…”

Section: Dynamics On Networkmentioning

confidence: 99%

“…The power of the MSF is that not single network realizations have to be considered but that whole classes of network topologies can be studied by investigating their eigenvalue spectrum. On several occasions the master stability function has been used to study synchrony in neural networks [Dhamala et al, 2004;Rossoni et al, 2005;Belzig, 2005;Lehnert et al, 2011a;Keane et al, 2012]. Frequently, models employed in neuroscience are of integrate-and-fire type meaning that the membrane voltage is set back to a resting potential after reaching a threshold.…”

Section: Dynamics On Networkmentioning

confidence: 99%

“…The MSF is only applicable to networks of identical nodes and only if the delay between all node pairs is identical, where the delay can be one discrete delay time [Dhamala et al, 2004;Lehnert et al, 2011a;Keane et al, 2012;Schöll, 2013] or a delay kernel [Kyrychko et al, 2014;Wille et al, 2014]. Only in the case of commuting coupling matrices two or several discrete delay times can be taken into account Dahms et al, 2012].…”

Section: Dynamics On Networkmentioning

confidence: 99%

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Controlling Synchronization Patterns in Complex Networks

Lehnert¹

2016

Springer Theses

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In this thesis, I consider the control of synchronization in delay-coupled complex networks. As one main focus, several applications to neural networks will be discussed. In the first part, I focus on the stability of synchronization in complex networks meaning that the control is realized by considering the stability of synchrony in dependence on the parameters. In the second part, adaptive control of synchronization is studied. To this end, adaptive control algorithms are developed that tune the system parameters such that the desired control goal is reached.Besides zero-lag synchrony -a state where all nodes follow the same dynamics without a phase lag -groups and cluster states are considered, i.e., states where the network consists of several groups where the nodes within one group are in zero-lag synchrony and, in the case of cluster synchrony, with a constant phase lag between the clusters.The stability of synchronization can be accessed via the master stability function [Pecora and Carroll, 1998]. This convenient tool allows for treating the node dynamics and the network topology in two separate steps, and, thus, allows for a quite general treatment of different network topologies. In this thesis, I will discuss the generalization of the master stability function to group and cluster states and to non-smooth systems.The master stability function can be used to investigate synchrony in neural networks. Neurons are excitable systems where type-I and type-II excitability can be distinguished. Here, the stability of synchrony for both types in complex networks with excitatory and inhibitory links is investigated on two generic models, namely the normal form of the saddle-node infinite period bifurcation and the FitzHugh-Nagumo system. Furthermore, synchronization in systems with heterogeneous delays or node parameters is studied.In situations where parameters are unknown or drift, adaptive control methods are useful since they allow for an automatically realized adaption of the control parameters. A convenient adaptive method is the speed-gradient method that minimizes a predefined goal function [Fradkov, 1979[Fradkov, , 2007. I first apply this method in the control of an unstable focus and an unstable periodic orbit embedded in the Rössler attractor. Furthermore, I show that clusters states in networks of delayed coupled Stuart-Landau oscillators can be controlled by adaptively tuning the phase of the complex coupling strength or by adapting the topology. The first method is particularly simple because only one parameter has to be adapted, while the second method is more reliable in the sense that its success is widely independent of the choice of the control parameters and the initial conditions. ZUSAMMENFASSUNGIn dieser Arbeit wird die Kontrolle von Synchronisation in komplexen Netzwerken mit retardierten Kopplungen untersucht. Dabei werden verschiedene Anwendungen auf neuronale Netzwerke diskutiert. Der erste Teil der Arbeit beschäftigt sich mit der Stabilität von Synchronisation in komplexen Ne...

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Synchronisation und komplexe Dynamik von Oszillatoren mit verzögerter Pulskopplung

2012

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Finger am Puls: Eine systematische experimentelle Studie von pulsgekoppelten chemischen Oszillatoren mit Zeitverzögerung bestätigt überraschend viele theoretische Vorhersagen zum dynamischen Verhalten eines Paares pulsgekoppelter Oszillatoren, wie z. B. das Auftreten von gegenphasigen (AP) und phasengleichen Oszillationen (IP), komplexe „Bursting“‐Oszillationen (C) und Oszillatorunterdrückung (OS). Die Ergebnisse sind relevant für die Neurowissenschaften und andere biologische Disziplinen.

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Loss of synchronization in complex neuronal networks with delay

Cited by 60 publications

References 36 publications

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

Controlling Synchronization Patterns in Complex Networks

Synchronisation und komplexe Dynamik von Oszillatoren mit verzögerter Pulskopplung

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