scholarly journals Time-delayed feedback in neurosystems

2009 ◽  
Vol 367 (1891) ◽  
pp. 1079-1096 ◽  
Author(s):  
Eckehard Schöll ◽  
Gerald Hiller ◽  
Philipp Hövel ◽  
Markus A Dahlem
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Coupling Strength ◽  
Delay Time ◽  
Feedback Loop ◽  
Time Synchronization ◽  
Delayed Feedback ◽  
Amplitude Death ◽  
Large Delay ◽  
Time Delayed Feedback

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh–Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.

TIME-DELAYED FEEDBACK IN A NET OF NEURAL ELEMENTS: TRANSITION FROM OSCILLATORY TO EXCITABLE DYNAMICS

2007 ◽  
Vol 07 (03) ◽  
pp. L225-L229 ◽  
Author(s):  
M. GASSEL ◽  
E. GLATT ◽  
F. KAISER
Keyword(s):  
Stability Analysis ◽  
Pattern Formation ◽  
Linear Stability Analysis ◽  
Delay Time ◽  
Additive Noise ◽  
Delayed Feedback ◽  
Amplitude Death ◽  
Global Oscillation ◽  
Feedback Strength ◽  
Time Delayed Feedback

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) via time-delayed feedback for properly chosen delay time and feedback strength. The result of a linear stability analysis fits very well to the simulations. In the amplitude death regime, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.

Control of multi-scroll attractors in a memristor-coupled resonator via time-delayed feedback

2018 ◽  
Vol 32 (32) ◽  
pp. 1850399 ◽  
Author(s):  
Zhilong Liu ◽  
Fuqiang Wu ◽  
Faris Alzahrani ◽  
Jun Ma
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Magnetic Flux ◽  
Memory Effect ◽  
Delayed Feedback ◽  
Feedback Gain ◽  
Initial Setting ◽  
Physical Background ◽  
Time Delayed Feedback ◽  
With Memory

A four-variable dynamical system composed of memristor is proposed to investigate the dependence of multi-scroll attractor on initial setting for one variable with memory, and the description for physical background is supplied. It is found that appropriate setting of initial values for the memory variable can induce different numbers of attractor, as a result, resetting initials can change the profile of attractors which is also dependent on the calculating period. Time-delayed feedback is used to stabilize the dynamical system thus the effect of initial dependence is suppressed and multi-scroll attractors are controlled by applying appropriate time delay and feedback gain in the controller. Furthermore, the system is verified on FPGA circuit platform and memristor is used to describe the memory effect of variable related to magnetic flux. It is confirmed that multi-scroll attractors can be stabilized and the dependence of initials setting is suppressed in experiment way.

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

Hidden data transmission based on time-delayed feedback system with switched delay time

2012 ◽  
Vol 38 (1) ◽  
pp. 51-54 ◽  
Author(s):  
V. I. Ponomarenko ◽  
A. S. Karavaev ◽  
E. E. Glukhovskaya ◽  
M. D. Prokhorov
Keyword(s):  
Data Transmission ◽  
Delay Time ◽  
Feedback System ◽  
Delayed Feedback ◽  
Hidden Data ◽  
Time Delayed Feedback

The Homicidal Chauffeur Problem With Time Delayed Feedback

2003 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi ◽  
Ali Fuat Ergenc
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Target Tracking ◽  
Critical Parameter ◽  
Delayed Feedback ◽  
Control Law ◽  
Pursuit Evasion ◽  
Parking Lot ◽  
Homicidal Chauffeur ◽  
Time Delayed Feedback

The classical pursuit-evasion scenario (target tracking) is studied with an interesting perspective. A homicidal chauffeur (pursuer) tries to capture an evader on a 2-dimensional platform (a parking lot). It utilizes a certain feedback control law, which enables the capture. If, however, a time delay is introduced for the sensory perception of the pursuer the performance of the pursuer can show dramatic changes. It may or may not capture its victim depending on this very critical parameter, the sensory time delay. The unique perspective is introduced at this feature.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

Stochastic resonance in deformable potential with time-delayed feedback

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200234 ◽  
Author(s):  
Y. J. Wadop Ngouongo ◽  
M. Djolieu Funaye ◽  
G. Djuidjé Kenmoé ◽  
T. C. Kofané
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Brownian Particle ◽  
Delayed Feedback ◽  
Memory Effects ◽  
Loop Area ◽  
Feedback Strength ◽  
Hysteresis Loop Area ◽  
Time Delayed Feedback ◽  
With Memory

This paper reports the stochastic resonance (SR) phenomenon with memory effects for a Brownian particle in a potential whose shape is subjected to deformation. We model the deformation in the system by the Remoissenet–Peyrard potential and the memory effects by the time-delayed feedback. The question of the possible influence of time-delayed feedback on the occurrence of SR is then of our interest. We examine numerically the effect of feedback strength as well as time delay on SR phenomenon in terms of hysteresis loop area. It is found that time-delayed feedback has a significant effect on SR and can induce double resonances in the system. We show that the properties of SR are varying, depending on interdependence between feedback strength, time delay and shape parameter. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

High-speed optical secure communication with an external noise source and an internal time-delayed feedback loop

2019 ◽  
Vol 7 (11) ◽  
pp. 1306 ◽  
Author(s):  
Yudi Fu ◽  
Mengfan Cheng ◽  
Xingxing Jiang ◽  
Quan Yu ◽  
Linbojie Huang ◽  
...  
Keyword(s):  
Secure Communication ◽  
High Speed ◽  
Feedback Loop ◽  
Noise Source ◽  
External Noise ◽  
Delayed Feedback ◽  
Internal Time ◽  
Time Delayed Feedback

SYNCHRONIZATION IN A RING OF UNIDIRECTIONALLY COUPLED FITZHUGH–NAGUMO NEURONS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450009 ◽  
Author(s):  
ANINDITA BHATTACHARJEE ◽  
M. K. DAS ◽  
SUBHENDU GHOSH
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Delayed Feedback ◽  
Feedback Gain ◽  
Model Parameters ◽  
Constant Input ◽  
Synchronization Phenomenon ◽  
Error Dynamics ◽  
Chemical Synapses

Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.

Controlling biological networks by time-delayed signals

2010 ◽  
Vol 368 (1911) ◽  
pp. 439-454 ◽  
Author(s):  
Gábor Orosz ◽  
Jeff Moehlis ◽  
Richard M. Murray
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Biological Networks ◽  
Biological Systems ◽  
Delayed Feedback ◽  
Use Of Time ◽  
Transcriptional Regulatory ◽  
Time Delayed Feedback ◽  
Control Tool

This paper describes the use of time-delayed feedback to regulate the behaviour of biological networks. The general ideas on specific transcriptional regulatory and neural networks are demonstrated. It is shown that robust yet tunable controllers can be constructed that provide the biological systems with model-engineered inputs. The results indicate that time delay modulation may serve as an efficient biocompatible control tool.

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