Speaker
Description
Time delays are often present in natural and technological processes, and can be essential for the precise understanding and description of important phenomena. On the other hand, chemical reaction networks (CRNs) provide a general framework for describing general nonnegative nonlinear dynamics. It is known that complex balance is a property of fundamental importance, which guarantees a strong robust stability for CRNs. It was proved in the 2010's that delayed complex balanced CRNs with mass action kinetics are asymptotically stable for arbitrarily large discrete delays and also for any practically meaningful distributed delay. In this contribution, these results are extended to CRNs with general non-mass-action kinetics having a product structure. The applicable reaction rates include e.g., Michaelis-Menten and Hill kinetics. It is shown that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is locally asymptotically stable relative to the class. The stability of the equilibria is shown using appropriate logarithmic Lyapunov–Krasovski functionals both in the discrete and the distributed delay case. The results further underline the importance of complex balance in the theory of general dynamical systems.
