Vibe is a Java-based simulator, but you now have Java turned off. You may turn on Java at any time.

 

 

 

Relaxation Oscillators:

 

Other Categories:

 

 

 

Vibe:Relaxation Oscillators:Fitzhugh Nagumo Oscillator

The Fitzhugh-Nagumo equations were derived simultaneoulsly by Fitzhugh and Nagumo et.al.
  • R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membranes, 1182-Biophys. J., 1 (1961), pp. 445--466. and
  • J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating 1214-nerve axons, Proc. IRL, 50 (1960), pp. 2061--2070.
These equations provide a fairly detailed picture of the action potential of a neuron. Here is the system of first-order differential equations which describes the Fitzhugh-Nagumo oscillator:

Like all relaxation oscillators, this oscillator has a slow accrual phase and a fast release phase. Here, v is voltage and w is recovery of voltage. Note that gamma is a shunting variable, and that theta is a thresholding variable. An explanation of shunting and thresholding is outside of the scope of Vibe.

A very important variable epsilon represents the coupling between the slow and fast phases. As epsilon increases, so does frequency. The variable omega is constant voltage and is held constant in Vibe at .112. Some voltage is required at all times to keep this oscillator going else the system becomes a point-attractor.

What is a neuron?
A neuron is a nerve cell, and is the primary building block of our nervous systems. Neurons have branches called axons which communicate with other neurons by sending them pulse-like electrical signals. Thes signals are picked up by the receiving neuron on small nodules called dendrites. When a neuron receives enough electrical input from its neigbors it will fire, sending off its own electrial pulse. Once fired, the neuron must recover before firing again. The slow collection and quick release of voltage is called integrate and fire behavior. The inability for the neuron to collect voltage immediatly after firing is called depolarization. This entire sequence (integrate, fire, rest) is called a neuron's action potential. With enough voltage and the right settings, the Fitzhugh-Nagumo model creates nice action potentials.


Vibe Oscillator Simulator © 2000-2003 Douglas S. Eck.
Back to the Vibe Home Page § Back to Douglas Eck's Home Page
Thu Jul 24 09:12:34 EDT 2003