Dissipative Structures In Chemical Reaction System

Dissipative structure is a new subject developed in the 1990s, the primary content of which contains the structure and characteristic of non-equilibrium opening system. This theory has great impact on many fields of natural science and social science such as physics, astronomy, biology, economics, and philosophy.In this paper, space-time dissipative structures of Brusselator model are studied in detail by using the bifurcation theory.Firstly, we study sphere structure of Brusselator Model in the fixed boundary condition, and have the numerical analysis of space-time dissipative structures of spherically symmetric structure, axially symmetric structure and spherically symmetric breaking respectively. The results show that under the appropriate parameters, if the critical value of control parameter that the first branch point corresponds to is Bc, the original steady structure becomes unstable and presents the spherically symmetric ordered structure after crossing it, and if this parameter is B1, the structure presents the spherically symmetric structure and changes over time periodically after crossing it, and if this parameter is Bc', the structure occurs symmetry breaking and presents the axially symmetric ordered structure after crossing it, and if this parameter is B1', the structure presents the axially symmetric structure and changes over time periodically after crossing it. These conclusions have certain significance in investigation of nuclear-type structures in biological and biochemical phenomena.Then, we study column structure of Brusselator Model in the fixed boundary condition, and have the numerical analysis of space-time dissipative structures of column symmetric structure and column symmetric breaking respectively. The results show that under the appropriate parameters, if the critical value of control parameter that the first branch point corresponds to is Bn'm', the original steady structure becomes unstable and presents the column symmetric ordered structure after crossing it, and if this parameter is B11, the structure presents the column symmetric structure and changes over time periodically after crossing it, and if this parameter is Bm'i'n', the structure occurs symmetry breaking and presents the new ordered structure after crossing it, and if this parameter is B111, the structure presents the new ordered structure and changes over time periodically after crossing it. The conclusions we have drawn provide useful reference for the evolution of the practical systems, especially the column-type structures of biological systems.Our studies on sphere structure and column structure of Brusselator Model will open a new situation for understanding the practical application of dissipative structure.