Spatial bifurcation

Spatial bifurcation is a form of bifurcation theory. The classic bifurcation analysis is referred to as an ordinary differential equation system, which is independent on the spatial variables. However, most realistic systems are spatially dependent. In order to understand spatial variable system (partial differential equations), some scientists try to treat with the spatial variable as time and use the AUTO package get a bifurcation results.[1][2]

The weak nonlinear analysis will not provide substantial insights into the nonlinear problem of pattern selection. To understand the pattern selection mechanism, we exploit first the method of spatial dynamics,[3] which was found to be an effective method exploring the multiplicity of steady state solutions.[2][4]

See also

References

  1. ↑ Wang, R.H., Liu, Q.X., Sun, G.Q., Jin, Z., and Van de Koppel, J. 2010. Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds. Journal of the Royal Society Interface, 6(37):705–18
  2. ↑ 2.0 2.1 A Yochelis et al The formation of labyrinths, spots and stripe patterns in a biochemical approach to cardiovascular calcification, 2008 New J. Phys. 10 055002
  3. ↑ Champneys A R 1998 Physica D 112 158–86
  4. ↑ Knobloch E 2008 Nonlinearity 21 T45–60