Reaction networks multiscale

Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited... 

If the reader can use these properties (when it is necessary) without additional clarification, it is possible to skip reading Section 3 and go directly to more applied sections. In Section 4 we study static and dynamic properties of linear multiscale reaction networks. An important instrument for that study is a hierarchy of auxiliary discrete dynamical system. Let A, be nodes of the network ("components"), Ai Aj be edges (reactions), and fcy,- be the constants of these reactions (please pay attention to the inverse order of subscripts). A discrete dynamical system

dynamical system for a given network we find for each A,- the maximal constant of reactions Ai Af k ( i)i>kji for all j, and — i if there are no reactions Ai Aj. Attractors in this discrete dynamical system are cycles and fixed points. 

Let us describe the possible location of the ergodicity boundary in the general multiscale reaction network (ifl. After deletion of reactions with constants fcy,j,kj from the network two ergodic components (minimal sinks) appear, Gi and Gz- The ergodicity boundary starts in one of the ergodic components, say Gi, and ends at the such a reagent B that another ergodic component, Gz, is reachable by B (there exists an oriented path from B to some element of Gz). 

A.N. Gorban and O. Radulescu, Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited Liqiu Wang, Mingtian Xu, and Xiaohao Wei, Multiscale Theorems... 

C.J. van Duijn, Andro Mikelic, I.S. Pop, and Carole Rosier, Effective Dispersion Equations for Reactive Flows with Dominant Peclet and Damkohler Numbers Mark Z. Lazman and Gregory S. Yablonsky, Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series A.N. Gorban and O. Radulescu, Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited... 

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