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Citation: Gao Senquan, Li Rusheng. TRANSITION FROM MULTIPLE STEADY STATES TO CHEMICAL OSCILLATION THROUGH A COMPLICATED SINGULAR POINT[J]. Acta Physico-Chimica Sinica, ;1986, 2(02): 160-165. doi: 10.3866/PKU.WHXB19860210 shu

TRANSITION FROM MULTIPLE STEADY STATES TO CHEMICAL OSCILLATION THROUGH A COMPLICATED SINGULAR POINT

Gao Senquan ,
Li Rusheng

1.
Department of Chemistry and Chemical Engineering, Tsinghua University, Beijing

Received Date: 10 May 1985
Available Online: 15 April 1986

Based on the results of phase plane analysis in paper I and using the technique of linear stability analysis and numerical simulation, the dynamic be- haviour of Schlögl model in CSTR is further analysed. It is shown that, with in- creasing the input concentration x° of species X but fixing the values of other parameters, the system may under the bifurcation from one steady state to three steady states and in turn to one steady state again, shown as in Fig.2.
Linear stability analysis shows that only one of the three branches of steady states for A<x°<B is stable. This stability feature may endow the system such an interesting behaviour that when the value of x° passes through point B, the transition from steady state on branch (1) to oscillatory state around branch (2) is discontinuous and abrupt, that is, the system transits abruptly from a steady stase to an oscillatory state with finite amplitude. On the other hand, the transition from oscillatory state to steady one (or inverse transition) is smooth and continuous when the value of x° passes through point C.
From the point of view of bifurcation theory, above discontinuous transiton belongs the saddle-node transition, that is, the saddle point and node approach each other, merge into one compliated multiple singular point, and finally disappear and a limit cycle apears. This result would be helpful for explaination of some abrupt transition phenomena between steady state and oscillatory stte observed in some physical-chemical systems, such as B-Z reaction system.
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