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Related Concept Videos

Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Propagation of Action Potentials01:23

Propagation of Action Potentials

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Damped Oscillations01:07

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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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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.
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Stability of Equilibrium Configuration01:23

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Related Experiment Video

Updated: Jun 23, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

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Published on: June 29, 2018

Activity patterns in networks stabilized by background oscillations.

Frank Hoppensteadt1

  • 1Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. frank.hoppensteadt@nyu.edu

Biological Cybernetics
|May 2, 2009
PubMed
Summary
This summary is machine-generated.

Background brain oscillations stabilize neural activity. This neuroengineering study shows how oscillation frequencies create distinct states, enabling persistent firing patterns and organized behavior in neural networks.

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Electronic Engineering

Background:

  • The brain functions within a dynamic, oscillatory environment.
  • Stable, organized neural behavior can emerge from these oscillations.
  • Analogous to stabilizing an inverted pendulum with oscillation.

Purpose of the Study:

  • Investigate how background oscillations create stable, organized behavior in neuro-oscillator arrays.
  • Demonstrate the role of oscillation frequencies in state space partitioning.
  • Explore the stabilization of persistent neural activity.

Main Methods:

  • Utilized electronic circuit arrays inspired by neuroengineering.
  • Analyzed the effect of background oscillation frequencies on system dynamics.
  • Examined state space partitioning into distinct basins of attraction.

Main Results:

  • Background oscillation frequencies partition the state space into distinct basins of attraction.
  • Persistent neural activity, otherwise unobservable, can be stabilized.
  • Organized behaviors are sustained by background oscillations and categorized by basins of attraction.

Conclusions:

  • Background oscillations are crucial for generating and stabilizing organized neural behavior.
  • Oscillation frequencies dictate the emergent behaviors and their persistence.
  • This mechanism offers insights into neural information processing and memory.