Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

Selivanov, Anton; Lehnert, Judith; Dahms, Thomas; Hövel, Philipp; Fradkov, Alexander L.; Schöll, Eckehard

doi:10.1103/physreve.85.016201

Cited by 103 publications

(56 citation statements)

References 28 publications

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“…Inducing again the change of coordinates x ¼ ðT I n Þ x and :¼ ðT I n Þ with T as in (33), the closedloop system is written as…”

Section: Local Analysismentioning

confidence: 99%

“…In the same spirit, in Ref. 33, the authors use the speed-gradient method to solve the synchronization problem in networks of time-delayed coupled Stuart-Landau oscillators. However, in all these papers, the authors impose strong conditions on the systems, i.e., they have to be fully actuated and/or the complete state must be available for feedback.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Murguía

Fey

Nijmeijer

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. This manuscript focuses on controlled synchronization of identical nonlinear systems interacting on networks with general topologies and interconnected through predictorbased diffusive dynamic couplings. The systems are said to be diffusively coupled, if they interact through weighted differences of the form c(y j À y i ) with some positive constant c called the coupling strength and y i , y j denoting the outputs of the ith and jth systems. An important element of our control scheme is the use of a communication network. Network communication is necessary in the study of synchronization to transmit and receive measurement and control data among the systems. Because of the time needed to transmit data over the network, the use of networked communication to exchange information results in unavoidable time-delays. This networked-induced delays are undesirable because they may lead to the loss of synchrony. Hence, when studying synchronization among dynamical systems with networked communication, it is important to design control algorithms which are robust with respect to time-delays. The results presented here follow the same research line as Refs. 1 and 2, where sufficient conditions for synchronization of diffusively interconnected nonlinear systems with and without time-delays are derived. In order to derive their results, the authors assume that the individual systems are semipassive 3 with respect to the coupling variable y i , and their corresponding internal dynamics have some desired stability properties (convergent internal dynamics 4 ). In particular, in Ref. 2, the authors study the problem of network synchronization of diffusively timedelayed coupled semipassive systems. They prove that under some mild assumptions, there always exists a region S in the parameter space (coupling strength c versus time-delay s), such that if ðc; sÞ 2 S, the systems synchronize. Nevertheless, it is important to note that for this class of systems, once the network topology is specified, the re...

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“…Inducing again the change of coordinates x ¼ ðT I n Þ x and :¼ ðT I n Þ with T as in (33), the closedloop system is written as…”

Section: Local Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Murguía

Fey

Nijmeijer

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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show abstract

“…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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“…The dynamics of the leader system approximates well the dynamics of the synchronized network (17) which can easily be seen by comparing Eq. (19) with Eq.…”

Section: =1mentioning

confidence: 73%

Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture

et al. 2016

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We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here, we develop a controller to counteract the impact of these heterogeneities. We first analyze the stability of the equilibrium point in a ring network of heterogeneous nodes. We then derive a sufficient condition for synchronization in the absence of control. Based on these results we derive the controller providing synchronization for parameter values where synchronization without control is absent. We demonstrate our results in networks with different topologies. Particular attention is given to hierarchical (fractal) topologies, which are relevant for the architecture of the brain.

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Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

Cited by 103 publications

References 28 publications

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

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

Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture

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