Symmetry breaking of temperature field in spatially distributed pure dissipative systems induced by chemical reaction diffusion heat conduction couplings is analyzed in this paper.

While a boundary of segmentlike are existed,a new symmetry breaking mechanism can be established with defining of the boundary conditions.

Since the 1940 s,the study of complex system science shows out that from inorganic material world to organic life world even to the complex social economical world are all of the process of from disorder to order,with which the main dynamical cause is symmetry breaking.

Through studying the broken symmetry, which is resulted from the differ.

Some qualitative relations between broken symmetry,broken ergodicity and order parameter space are exposed;through them a more fundamental understanding of concepts such as phase transition,meta equilibrium phase is hoped and this makes the thermodynamics and statistical dynamics more coherently related.

It is based on Cheng-Born theory of broken symmetry and TFDC(Thomas-Fermi-Dirac-Cheng) electron theory.

The theory and algorithm of symmetry-breaking bifurcation are applied to finding multiple solutions to the boundary value problem of the Henon equation.

The theory and algorithm of symmetry-breaking bifurcation are applied to finding multiple solutions for boundary value problems of nonlinear elliptic PDE s, different symmetry properties of nontrivial solutions have been studied, and numerical multiple solutions which have vary symmetry properties bifurcating from bifurcation points are visualized.

We choose D_(10) equivariant Brusslator reaction problem as the research model because of its abundant bifurcation phenomenon and the symmetry-breaking bifurcation theory are used to computing the solu.