Chemical reaction networks with finite attractor regions

Abstract

This paper gives a test which establishes that a chemical reaction network has a finite globally attracting region in concentration space for a particular set of rate constants. A second test can establish the same conclusion for all sets of rate constants. If a network passes either test and all the steady states of the system are unstable, there must exist some exotic attractor such as a limit cycle, torus, or chaos either for the set of rate constants used or for all sets of rate constants. A computer algorithm for applying the test is developed.