From oscillations to excitability: A case study in spatially extended systems

S. C. Muller1, P. Coullet, D. Walgraef

  • 1Max-Planck-Institut fur molekulare Physiologie, Rheinlanddamm 201, D-44139 Dortmund, GermanyInstitut Non Lineaire de Nice, Universite de Nice-Sophia Antipolis, 1361 Route des Lucioles, F-06560 Valbonne, FranceCenter for Nonlinear Phenomena and Complex Systems, Free University of Brussels, CP 231, B-1050 Brussels, Belgium.

Chaos (Woodbury, N.Y.)
|September 1, 1994
PubMed
Summary

This volume explores spatiotemporal patterns in self-oscillatory and excitable systems. It investigates the transition from oscillatory to excitable behavior and its impact on spiral waves in active media.

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...
Damped Oscillations01:07

Damped Oscillations

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.
Although friction and other non-conservative...
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.
Oscillations In An LC Circuit01:31

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
Action Potential: Phases of Stimulation01:28

Action Potential: Phases of Stimulation

The action potential is a complex electrical event that occurs in excitable cells, such as neurons and muscle cells. It consists of several distinct phases, each with specific characteristics.
Resting Phase:
In this phase, the cell's membrane is at its resting potential, typically around -70 millivolts (mV) for neurons. Inside the cell, there is a higher concentration of potassium ions (K+) and a lower concentration of sodium ions (Na+). Voltage-gated sodium channels are closed, and...
Propagation of Action Potentials01:23

Propagation of Action Potentials

The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...