Using the Liapunov-Schmidt reduction and the symmetry-breaking bifurcation theories,we compute and visualize the D4-symmetric positive solutions of the boundary value problem of the Chandrasekhar equation on the unit square of the plane.

Consequently the methods for computing the symmetry-breaking bifurcation are given and applied to the D6 equivariant Brusselator reaction problem.

The mechanism of the symmetry breaking bifurcation, a prerequisite for period-doubling bifurcations, is presented.

The system could undergo the period-doubling bifurcation,saddle-note bifurcation,symmetry-breaking bifurcation and so forth to chaos,as the control parameter was set on some certain intervals.

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.