Control of noise-induced oscillations by delayed feedback

Balanov, A. G.; Janson, Natalia B.; Schöll, Eckehard

doi:10.1016/j.physd.2004.05.008

Cited by 92 publications

(74 citation statements)

References 35 publications

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“…In the context of excitable systems, the effects of time-delayed feedback control on a FitzHugh-Nagumo (FHN) system driven by white noise have been studied in Balanov et al (2004), Janson et al (2004), Prager et al (2007) and *Author for correspondence (schoell@physik.tu-berlin.de).…”

Section: Introductionmentioning

confidence: 99%

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Brandstetter

Dahlem

Schöll

2010

Phil. Trans. R. Soc. A.

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The interplay of time-delayed feedback and temporally correlated coloured noise in a single and two coupled excitable systems is studied in the framework of the FitzHughNagumo (FHN) model. By using coloured noise instead of white noise, the noise correlation time is introduced as an additional time scale. We show that in a single FHN system the major time scale of oscillations is strongly influenced by the noise correlation time, which in turn affects the maxima of coherence with respect to the delay time. In two coupled FHN systems, coloured noise input to one subsystem influences coherence resonance and stochastic synchronization of both subsystems. Application of delayed feedback control to the coloured noise-driven subsystem is shown to change coherence and time scales of noise-induced oscillations in both systems, and to enhance or suppress stochastic synchronization under certain conditions.

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Section: Introductionmentioning

confidence: 99%

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Brandstetter

Dahlem

Schöll

2010

Phil. Trans. R. Soc. A.

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“…All methods mentioned above assume the presence of deterministic selfoscillating components in the dynamics, and aim either to enhance the latter component or to exploit the external deterministic oscillating force to manipulate the regularity of motion. In contrast to those investigations, a passive self-adaptive method for the control of oscillations induced merely by noise was proposed only recently [20,21]. It uses time-delayed feedback control to change the coherence of the oscillations, and tune their timescale.…”

Section: Introductionmentioning

confidence: 99%

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

et al. 2005

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We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

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“…9 In contrast to Ref. 8 and 9 where a single FitzHugh-Nagumo oscillator is analyzed, we study a network of N delaycoupled FitzHugh-Nagumo oscillators.…”

Section: Interplay Of Topology and Delayed Couplingmentioning

confidence: 99%

“…In particular, we are interested in the phenomena of coherence resonance 3,[8][9][10]12,13,17,[24][25][26][27][28][29][30][31][32][33] . Thus far, control of coherence resonance has been studied in single FitzHugh-Nagumo and in two coupled FitzHugh-Nagumo oscillators with time-delayed feedback 12 .…”

Section: Introductionmentioning

confidence: 99%

Coherence resonance in a network of FitzHugh-Nagumo systems: Interplay of noise, time-delay, and topology

Masoliver

Malik

Schöll

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible.The FitzHugh-Nagumo system is a paradigmatic model which describes the excitability and spiking behavior of neurons. It has various applications ranging from biological processes to nonlinear electronic circuits. In the excitable regime under the influence of noise, this model exhibits the counterintuitive phenomenon of coherence resonance. It means that there exists an optimum intermediate value of the noise intensity for which noise-induced oscillations become most regular. We investigate coherence resonance in a network of delaycoupled FitzHugh-Nagumo elements with local, nonlocal and global coupling topologies. Networks with nonlocal topology are inspired by neuroscience, as they emulate the observation that strong interconnections between neurons are typical within a certain range while fewer connections exist at longer distances. We illustrate that the interaction between the network topology, the time-delay in the coupling, and the noise leads to a rich oscillatory dynamics. In particular, we demonstrate that the regularity of this dynamics is controllable, i.e., one can enhance or weaken coherence resonance by varying the coupling and delay time.

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Control of noise-induced oscillations by delayed feedback

Cited by 92 publications

References 35 publications

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

Coherence resonance in a network of FitzHugh-Nagumo systems: Interplay of noise, time-delay, and topology

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