HodgkinHuxley Theory of Nerve Membranes:

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Hodgkin-Huxley Theory of Nerve Membranes

• FitzHugh-Nagumo Model

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Basic Mathematical Model
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Physical Equivalent Circuit
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Equations
V is potential INa, IK and IL are respectively
the sodium, potassium and leakage currents. The
gs are constant conductances. VNa, VK and VL are
constant equilibrium potentials. The m, n and h
are variables, bounded by 0 and 1.
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More Equations
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FitzHugh-Nagumo Model

• The time scales for m, n, h are not all of the
  same order
• The time scales for m, h are much faster
• Setting m, h to constants will still retain many
  features of the system
• This results in a 2 variable model in V and n

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The New 2 Variable System

• Dimensionless
• v is like V, w plays the role of m, n and h
• 0ltalt1, b and g are positive constants

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