The structure of slow invariant manifolds and their bifurcational routes in chemical kinetic models

详细信息    查看全文

• 作者：A. Adrover ; F. Creta ; S. Cerbelli ; M. Valorani ; M. Giona
• 关键词：Dynamical systems ; Invariant geometric properties ; Slow manifolds ; Geometric singular perturbation theory ; Multiple time scales ; Lyapunov numbers
• 刊名：Computers and Chemical Engineering
• 出版年：2007
• 出版时间：November 2007
• 年：2007
• 卷：31
• 期：11
• 页码：1456-1474
• 全文大小：954 K

文摘

This article analyzes the global geometric properties of slow invariant manifolds in two-dimensional chemical kinetic models. By enforcing the concept of Lyapunov-type numbers, a classification of slow manifolds into global and generalized structures is obtained, and applied to explain the occurrence of different dynamic phenomena. Several related concepts such as stretching heterogeneity and style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TFT-4MMPNK2-5&_mathId=mml124&_user=10&_cdi=5235&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=64fcc04dd2add27132da803da29c38cb"" title=""Click to view the MathML source"">α– style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TFT-4MMPNK2-5&_mathId=mml125&_user=10&_cdi=5235&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=8f7ebfe54e18e4b5d77f19806155edd6"" title=""Click to view the MathML source"">ω inversion are introduced and commented by taking the Semenov system as a paradigmatic example. We show that the existence of a global slow manifold along with its properties are controlled by a transcritical bifurcation of the points at infinity, that can be readily identified by analyzing the Poincaré projected (Pp) system. The information that can be obtained from the analysis of the Pp-system, and specifically the presence of saddle-points on the Poincaré circle, are extremely helpful in the construction of a complete picture of the structure and properties of slow invariant manifolds even when the system exhibits non-hyperbolic equilibrium points or stable limit cycles.