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Related Concept Videos

Effects of feedback01:24

Effects of feedback

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
Feedback control systems01:26

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Forced Oscillations01:06

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...

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Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
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Impact of nonlinear delayed feedback on synchronized oscillators.

Oleksandr V Popovych1, Christian Hauptmann, Peter A Tass

  • 1Institute of Neurosciences and Biophysics 3 - Medicine, Research Center Jülich, 52425 Jülich, Germany. o.popovych@fz-juelich.de

Journal of Biological Physics
|August 12, 2009
PubMed
Summary

Nonlinear delayed feedback controls synchronization in coupled oscillators, offering both synchronizing and desynchronizing effects. This method shows promise for treating neurological diseases linked to abnormal brain synchrony.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Neuroscience

Background:

  • Synchronization is crucial in coupled oscillator systems.
  • Abnormal synchrony is implicated in neurological disorders.
  • Controlling collective dynamics is a significant challenge.

Purpose of the Study:

  • To investigate the control of synchronization in large ensembles of coupled oscillators using nonlinear delayed feedback.
  • To explore the dual effects (synchronizing and desynchronizing) of nonlinear delayed feedback.
  • To propose nonlinear delayed feedback as a therapeutic strategy for neurological diseases.

Main Methods:

  • Mathematical modeling of mean-field dynamics for coupled oscillators.
  • Analysis of the existence and stability of feedback-induced states.
  • Exploration of multistability and dynamical properties of desynchronized states.

Main Results:

  • Nonlinear delayed feedback effectively controls synchronization processes.
  • The feedback exhibits both synchronizing and predominantly desynchronizing effects.
  • Stable, feedback-induced desynchronized states and their properties were identified.

Conclusions:

  • Nonlinear delayed feedback offers a powerful tool to manipulate collective dynamics in oscillatory systems.
  • The desynchronizing capacity of this feedback is particularly significant.
  • Nonlinear delayed feedback stimulation is a promising approach for treating neurological conditions associated with abnormal synchrony.