2013, XVIII, 314 p. 67 illus., 31 illus. in color.
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Overview of recent developments in the theory of nonautonomous dynamical systems
Examples of concepts and techniques in the context of simple models from the life sciences
Representative collection of nonautonomous dynamical systems in the life sciences
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Content Level »Research
Keywords »37B55,92XX,34C23,34C45,37HXX - Models from the life sciences - Nonautonomous bifurcations - Nonautonomous dynamical systems
Nonautonomous dynamical systems in the life sciences.- Random dynamical systems with inputs.- Canard theory and excitability.- Stimulus-response reliability of biological networks.- Coupled nonautonomous oscillators.- Multisite mechanisms for ultrasensitivity in signal transduction.- Mathematical concepts in pharmacokinetics and pharmacodynamics with application to tumor growth.- Viral kinetic modeling of chronic hepatitis C and B infection.- Some classes of stochastic differential equations as an alternative modeling approach to biomedical problems.