Bar & Eiswirth 1993

Key: bar1993turbulence

This simple two-variable model was created by modifying the model by FitzHugh & Nagumo to describe cardiac excitation waves. This model shows that spiral breakup, leading to turbulence, can occur in a two-dimensional reaction-diffusion system with delayed-inhibitor production.

References

  1. https://doi.org/10.1103/PhysRevE.48.R1635

Variables

  1. u = 0.0

  2. v = 0.0

Parameters

  • diffusivity_u = 1.0

  • eps = 0.075

  • a = 0.84

  • b = 0.07

Source code

OpenCL kernel
const Real _react_u = - u * (u - 1.0) * (u - ((v + b)/a) )/eps;
const Real f = (u < 1.0/3.0) ? 0.0 : (u > 1.0) ? 1.0 : (1 - 6.75*u*(u - 1)*(u - 1));
const Real _react_v = f - v;
*_new_u = u + dt * (_react_u + _diffuse_u);
*_new_v = v + dt * _react_v;

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- phenomenological