Computation of periodic orbits in a three-dimensional kinetic model of catalytic hydrogen oxidation
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Date
2002
Journal Title
Journal ISSN
Volume Title
Publisher
Selcuk University Research Center of Applied Mathematics
Access Rights
info:eu-repo/semantics/openAccess
Abstract
Aniterative method for solving periodical boundary-value problem (BVP) for autonomous ordinary differential equations (ODEs) is applied to calculations of periodic orbits and their stability in a three-dimensional kinetic model of catalytic hydrogen oxidation. According to the method, the periodic orbit is decomposed into pieces by local cross-sections {?i}{?i} and between ?i?i and ?i+1?i+1 the integration of the system is to be accomplished. Hence we obtain an $\alpha$-pseudo-orbit and then construct the generalized Poincare map. Thus the BVP for ODEs is reduced to a system of nonlinear algebraic equations that takes into account both the boundary conditions of periodicity and condition of the solution continuity at boundary points of pieces. Being linearized, the algebraic system has a band structure and for solving such a system the orthogonal sweep method is extremely effective. In the model considered we find numerically periodic orbits of rather complex structure, give an example of weakly stable dynamics, and show the role of successive period doubling bifurcations in the creation of weakly stable dynamics.
Description
Keywords
Periodic orbit, Numerical solution of ordinary differential equations, Chemical kinetic model, Period doubling bifurcation, Weakly stable dynamics
Journal or Series
Selcuk Journal of Applied Mathematics
WoS Q Value
Scopus Q Value
Volume
3
Issue
Citation
Chumakova, N. A., Chumakova, L. G., Kiseleva, A. V., Chumakov, G. A. (2002). Computation of periodic orbits in a three-dimensional kinetic model of catalytic hydrogen oxidation. Selcuk Journal of Applied Mathematics, 3 (1), 3-20.
