Continuous control of chaos by self-controlling feedback

Pyragas, K.

doi:10.1016/b978-012396840-1/50038-2

Cited by 198 publications

(284 citation statements)

References 15 publications

Supporting

Mentioning

274

Contrasting

Unclassified

Order By: Relevance

“…Delayed feedback control techniques were first developed by Pyragas (1992). Recently, the idea of Pyragas was extended to achieve a desynchronization in ensembles of coupled oscillators by Rosenblum and Pikovsky (2004).…”

Section: Discussionmentioning

confidence: 99%

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

2005

View full text Add to dashboard Cite

In detailed simulations we present a coordinated delayed feedback stimulation as a particularly robust and mild technique for desynchronization. We feed back the measured and band-pass filtered local filed potential via several or multiple sites with different delays, respectively. This yields a resounding desynchronization in a naturally demand-controlled way. Our novel approach is superior to previously developed techniques: It is robust against variations of system parameters, e.g., the mean firing rate. It does not require time-consuming calibration. It also prevents intermittent resynchronization typically caused by all methods employing repetitive administration of shocks. We suggest our novel technique to be used for deep brain stimulation in patients suffering from neurological diseases with pathological synchronization, such as Parkinsonian tremor, essential tremor or epilepsy.

show abstract

Section: Discussionmentioning

confidence: 99%

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

2005

View full text Add to dashboard Cite

show abstract

“…Typically, the feedback signal is proportional to the deviation of a coordinate of the systems from the desired state (proportional control), or to the derivative of the coordinate (proportional-derivative control), or to the integral of the coordinate over the past (proportional-integral control), or to a combination of these three values [40]. Another group of stabilization techniques uses linear or nonlinear time-delayed feedback, see, e.g., [41][42][43][44]. For low-dimensional systems, the theory of feedback stabilization is well-developed and finds many technical applications.…”

Section: What Does the Control Theory Say?mentioning

confidence: 99%

“…An application of delayed feedback control has become quite popular since publication of Pyragas' paper on stabilization of periodic orbits in chaotic systems [41]. This method has been studied quite intensively [50], moreover it has been recently extended to a problem of a control of chaos coherence [51].…”

Section: Delayed Feedback Controlmentioning

confidence: 99%

Controlling Collective Synchrony by Feedback

Rosenblum

Pikovsky

2008

Reviews of Nonlinear Dynamics and Complexity

View full text Add to dashboard Cite

What is Collective Synchrony?Synchronization is a general nonlinear phenomenon which can be briefly described as an adjustment of rhythms of self-sustained oscillatory systems due to their interaction [1]. In the simplest setup, two periodic oscillators of this class can adjust their phases and frequencies, even if the coupling between the systems is very weak. This effect is often called phase locking or frequency entrainment. The concept can be generalized to the case of many oscillating objects with a variety of different coupling configurations: oscillating subsystems can be placed on a regular lattice, or organized in a complex, possibly irregular, network, or form a continuous medium. If an oscillating unit is interacting with its neighbors only, then synchronization typically appears in a form of waves or oscillatory modes. Contrary to this, if the interaction is a long-range one, then global synchrony, where all or almost all units oscillate in pace, can set in. Examples of synchronous dynamics range from mechanical systems like pendulum clocks [2, 3] and metronomes [4], through modern physical devices, e.g., Josephson junctions and lasers (see [5,6] and references therein) to live systems (see, e.g., a review [7]), including human beings [8,9]. The mostly popular model, describing collective dynamics in a large population of self-sustained oscillators is that of globally (all-to-all) coupled units. This framework has been used to describe many physical, biological, and social phenomena. The main effect observed in these models is the collective synchrony, when a large part or all units adjust their rhythms and produce a nonzero mean field, which has the same frequency as the synchronized majority. In the simplest setup this state appears from the fully asynchronous one via the Kuramoto transition [10,11]: if the coupling strength ε in the ensemble exceeds some threshold value ε cr , the macroscopic mean field appears and its amplitude growth with the super-criticality ε − ε cr . This transition is often considered in an analogy to second order phase transitions; on the other hand, it can be viewed at as a supercritical Hopf bifurcation for the mean field.

show abstract

“…9, d is a control parameter that modulates the eect of internal-external stimulation on the Encoder Module's current activation; m is the novelty sensitivity parameter (Heath & Fulham, 1988), which also modulates the eect of internal-external stimulation on the control process. This control technique was inspired by a similar feedback control procedure devised by Pyragas (1992) to stabilise unstable periodicities within chaotic systems.…”

Section: A Controlled Nonlinear Neural Networkmentioning

confidence: 99%

The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics

Heath

2000

Psychological Research Psychologische Forschung

View full text Add to dashboard Cite

The Ornstein-Uhlenbeck (OU) model for human decision-making has been successfully applied to account for response accuracy and response time (RT) data in recent two-choice decision models. A variant of the OU model is shown to arise from the response dynamics of a nonlinear network consisting of randomly connected neural processing units. When feedback control of the network is effected by the stimulus onset, the average network response is an autocorrelated random signal satisfying the stochastic differential equation for the OU process. An alternative, more general, stimulus detection procedure is proposed which involves the use of an adaptive Kalman filter process to track any temporal change in autoregressive parameters. The predicted decision time distributions suggest that both the OU and the Kalman filter processes can serve as alternative models for RT data in experimental tasks.

show abstract

Continuous control of chaos by self-controlling feedback

Cited by 198 publications

References 15 publications

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

Controlling Collective Synchrony by Feedback

The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics

Contact Info

Product

Resources

About