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Title: Periodic solutions and dynamics of a multimolecular reaction system
Authors: Kwek, K.H. 
Zhang, W.
Keywords: Bendixson's criteria
Biochemical kinetics
Degenerate equilibrium
Hopf bifurcation
Periodic solution
Issue Date: 2-Aug-2002
Citation: Kwek, K.H., Zhang, W. (2002-08-02). Periodic solutions and dynamics of a multimolecular reaction system. Mathematical and Computer Modelling 36 (1-2) : 189-201. ScholarBank@NUS Repository.
Abstract: In this paper, we consider a general multimolecular reaction system, which appears in biochemistry as a theoretical problem of concentration kinetics and in mathematics as a special polynomial vector field of high degree. We shall investigate its global dynamics and discuss existence and nonexistence of periodic solutions. Although the case of trimolecular reactions and some other special cases were studied extensively, it remains difficult to discuss the general case, that there is involved a lot complicated computation for polynomials of any given degree. In this paper, special techniques are used in computation of Lyapunov numbers for Hopf bifurcation, construction of Dulac auxiliary functions for nonexistence of periodic solution, and determination of qualitative properties of degenerate equilibria. © 2002 Elsevier Science Ltd. All rights reserved.
Source Title: Mathematical and Computer Modelling
ISSN: 08957177
DOI: 10.1016/S0895-7177(02)00115-2
Appears in Collections:Staff Publications

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