Speaker: Dean Gull, Applied Mathematics
Title:
Time: 2:30 PM, Thursday, 5/17/07
Abstract:
A homeomorphic transformation is presented for deficiency zero chemical reaction systems that linearizes the derived dynamical system while faithfully maintaining local and global quantitative and qualitative properties. Thus demonstrating that the nonlinearities of this class of chemical reaction systems may be ignored without compromising the quantitative global dynamics. In particular, it will be shown that when the number of chemical species is less than or equal to the number of chemical complexes, then the linear and nonlinear topological spaces are homeomorphic. If however, there are more species than complexes, then the homeomorphism holds modulo an equivalence relation that defines topological fibers (submanifolds) of the nonlinear reaction phase-space manifold. This novel transformation is utilized to present an alternative proof of Feinberg's Deficiency Zero Theorem.
Everyone welcome!