一个简单的能呈现二分岔现象的双分子反应模型

A SIMPLE BIMOLECULAR REACTION MODEL GIVING RISE TO PITCHFORK BIFURCATION

二分岔现象(pitchfork bifurcation)是非平衡非线性动力系统中最典型和最简单的分岔现象.1972年Schlogl提出了如下一个化学反应模型: A+2x?3X,X?B (1)假定组份A和B的浓度可由外界控制为恒定,在某些条件下该模型可呈现出二分岔现象.自那以后,Schlogl模型已成为人们研究非平衡相变时最广泛采用的理论模型,该模型对推动非平衡非线性现象的研究起了十分重要的作用.但从物理-化学的角度来看,该模型存在着如下一些问题:首先该模型涉及一个三分子自催化反应步骤。

A simple reaction model; A+B→C+D, B+C→2B,D→A, is shown to be able to exhibit a pitchfork bifurcation of stationary states in a continuous stirred tank reactor (CSTR). To be different from the well-known Schlogl model, the present modelinvolves only mono-and bimolecular reaction steps and without an assumption ofpool chemicals which may cause an inequality of total mass for different statesin system and, in turn, some problems for comparison of thermodynamic propertiesfor different states.