Spatial bifurcation is a form of
bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations ...
. The classic bifurcation analysis is referred to as an
ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contras ...
system, which is independent on the spatial variables. However, most realistic systems are spatially dependent. In order to understand spatial variable system (
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
s), some scientists try to treat with the spatial variable as time and use the AUTO package get a bifurcation results.
The weak nonlinear analysis will not provide substantial insights into the nonlinear problem of
pattern selection. To understand the pattern selection mechanism, the method of spatial dynamics is used, which was found to be an effective method exploring the multiplicity of steady state solutions.
See also
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Spatial ecology
Spatial ecology studies the ultimate distributional or spatial unit occupied by a species. In a particular habitat shared by several species, each of the species is usually confined to its own microhabitat or spatial niche because two species in ...
*
spatial pattern
Spatiotemporal patterns are patterns that occur in a wide range of natural phenoma and are characterized by a spatial and a temporal patterning. The general rules of pattern formation hold. In contrast to "static", pure spatial patterns, the ...
References
Bifurcation theory
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