Dual Chemical Reaction Networks and Implications for Lyapunov-Based Structural Stability

Given a class of (bio)Chemical Reaction Networks (CRNs) identified by stoichiometric matrix S, we define as dual reaction network, CRN*, the transpose S T . We consider both dynamical systems describing time evolution species concentrations and rates. First, based on analysis Jacobian matrix, show that structural (i.e., parameter-independent) local stability properties are equivalent for CRN its CRN*. also assess global two networks, analysing concentration rate representations. prove existence polyhedral (or piecewise-linear) Lyapunov function in is to piecewise-linear rates CRN*; fact, if V CRN, xmlns:xlink="http://www.w3.org/1999/xlink">* network. finally how duality can be exploited gain additional insight into biochemical networks.