Analysis and Control of Polynomial Dynamic Models with Biological Applications

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems.

Describes and illustrates the relationship between the dynamical, algebraic and structural features of the quasi-polynomial (QP) and kinetic modelsShows the applicability of kinetic and QP representation in biological modeling and control through examples and case studiesEmphasizes the importance and applicability of quantitative models in understanding and influencing natural phenomena

1. Introduction 2. Basic Notions 3. Model Transformations and Equivalence Classes 4. Model analysis 5. Stabilizing feedback control design 6. Case studies

Appendix A. Notations and abbreviations B. Mathematical tools