Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes the 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). There is a significant emphasis on applications, which allows the reader to see the techniques in action. The book focuses on quasi-polynomial (QP, or generalized Lotka-Volterra) systems and kinetic systems (also called biochemical reaction networks or simply CRNs) since these are so-called universal descriptors for smooth nonlinear systems. This means that they can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems. Moreover, both system classes are really natural descriptors of biological and biochemical processes: QP systems are the generalizations of Lotka-Volterra models originally used for modelling general population dynamics and related phenomena, while kinetic systems composed of elementary reaction steps come from the description of (bio)chemical processes. The main practical advantage of QP and kinetic systems is their relatively simple matrix-based algebraic structure that allows the development of efficient computational (e.g. optimization-based) methods for their dynamical analysis and control. Additionally, a direct physical interpretation of many important system properties is often possible for these models.

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