Time-Delayed Feedback in a Net of Neural Elements: Transition From Oscillatory to Excitable Dynamics

Gassel, Martin; Glatt, Erik; Kaiser, F.

doi:10.1142/s0219477507003878

Cited by 29 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a variety of physical, engineering, biological, and chemical systems the presence of time-delayed feedback or time-delayed couplings is inevitable. Examples include propagation delays in networks [24], laser arrays [25][26][27], electronic circuits [28], and neural systems [29][30][31]. Time-delayed nonlinear systems are found to show interesting dynamical phenomena such as novel bifurcations [32,33], amplitude death [34], strange nonchaotic attractors [35], hyperchaos [36], stochastic dynamics [37][38][39], excitation regeneration [40], reentrance phenomena [41,42], and patterns [43].…”

Section: Introductionmentioning

confidence: 99%

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

2011

View full text Add to dashboard Cite

The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.

show abstract

Section: Introductionmentioning

confidence: 99%

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

2011

View full text Add to dashboard Cite

show abstract

“…Time delays are always present in coupled systems owing to the finite signalpropagation time. These time lags give rise to complex dynamics and have been shown to play a key role in the synchronization behaviour of neural systems (Hauschildt et al 2006;Gassel et al 2007;Dahlem et al 2009;Schöll et al 2009). Coupled lasers exhibit similar phenomena to coupled neurons and have attracted much attention owing to their importance in telecommunication applications (Wünsche et al 2005;Fischer et al 2006;Klein et al 2006;Shaw et al 2006;Landsman & Schwartz 2007;Flunkert et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Delay stabilization of periodic orbits in coupled oscillator systems

Fiedler

Flunkert

Hövel

et al. 2010

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

We study diffusively coupled oscillators in Hopf normal form. By introducing a noninvasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super-and subcritical cases, we state a condition on the oscillator's nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of oddnumber orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

show abstract

“…In particular, when the transmission delays are much smaller than the local processing delays, the fluctuations diverge as λτ o →π/4 [Eq. (17)].…”

Section: Discussion and Summarymentioning

confidence: 99%

The impact of competing time delays in coupled stochastic systems

2011

View full text Add to dashboard Cite

We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays at each element. We establish the scaling theory for the phase boundary of synchronization and for the steady-state fluctuations in the synchronizable regime. Further, we provide the asymptotic behavior near the boundary of the synchronizable regime. Our results also imply the potential for optimization and trade-offs in synchronization problems with time delays.

show abstract

Time-Delayed Feedback in a Net of Neural Elements: Transition From Oscillatory to Excitable Dynamics

Cited by 29 publications

References 12 publications

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Delay stabilization of periodic orbits in coupled oscillator systems

The impact of competing time delays in coupled stochastic systems

Contact Info

Product

Resources

About