Dynamical analysis of evolution equations in generalized models

Abstract

Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has been used successfully to answer applied questions. Yet their potential to facilitate analytical computations has not been realized in the mathematical literature. In the present paper we introduce the method of generalized modeling in mathematical terms, supporting the key steps of the procedure by rigorous proofs. Further, we point out open questions that are in the scope of present mathematical research and, if answered could greatly increase the predictive power of generalized models.

28 pages, 3 figures, revised version

References in corpus (5)

• Structural Kinetic Modeling of Metabolic Networks
• Generalized models as a universal approach to the analysis of nonlinear dynamical systems
• Boolean versus continuous dynamics on simple two-gene modules
• Local dynamical equivalence of certain food webs
• Nonlocal Generalized Models of Predator-Prey Systems

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