Nonautonomous dynamical systems in the life sciences (Q384824)

Mathematical sciences often are developed basing on the practical needs especially in our days. Real world phenomena and particularly the life sciences require the development of the theory of nonautonomous dynamical systems (NDS) random dynamical systems (RDS) and stochastic differential equations (SDEs). The reviewed collective monograph contains the selected proceedings of the workshop ``Nonautonomous and random dynamical systems in life sciences'' held in Inzell, Germany 01-05. August 2011. First three articles (Part I) are theoretical. The introductory contribution of the editors highlights key concepts of mathematical theory of deterministic nonautonomous dynamical systems (DS) and gives an review of their applications to various models of the life sciences. Chapter 2 is devoted to random DS with inputs by M. Marcondest de Freitas and E.D. Sontag describes the concept of a random DS extending it to problems with inputs and outputs and gives applications to feedback connections. Important part of DS in physiology consist the singularly perturbed DS on multiple time scales presented in the third article ``Canard theory and excitability'', by M. Wechselberg et. al. Part II of this collective monograph contains applications to the life sciences, mainly to mathematical biology: Ch. 4 ``Stimulus-Response Reliability of Biological Networks'' by Kevin K. Lin reviews some basic concepts and results from the ergodic theory of random DS and studies the reliability of networks; Ch. 5 ``Coupled Nonautonomous Oscillators'' by Ph. Clemson et al. includes novel methods suitable to reconstruct NDS at the usage data from a real living system by studying time-dependent coupling between cardiac and respiratory rhythms; Ch. 6 ``Multisite Mechanisms for Ultrasensitivity in Signal Transduction'' contains an review of molecular models with ultrasensitive behavior and three articles devoted to medical applications: ``Mathematical concepts in pharmacokinetics and pharmacodynamics with applications to tumor growth'', by G. Koch and J. Schropp, ``Viral kinetic model of chronic hepatitis C and B infection'', by E. Herrmann and Yu. Asai, and finally ``Some classes of stochastic DEs as an alternative modelling approach to biomedical problems'' by Christina and Nicolae Surulescu. The articles of this volume will be reviewed individually. Indexed articles: \textit{Kloeden, Peter E.; Pötzsche, Christian}, Nonautonomous dynamical systems in the life sciences, 3-39 [Zbl 1311.37075] \textit{De Freitas, Michael Marcondes; Sontag, Eduardo D.}, Random dynamical systems with inputs, 41-87 [Zbl 1311.37038] \textit{Wechselberger, Martin; Mitry, John; Rinzel, John}, Canard theory and excitability, 89-132 [Zbl 1319.34114] \textit{Lin, Kevin K.}, Stimulus-response reliability of biological networks, 135-161 [Zbl 1311.37009] \textit{Clemson, Philip T.; Petkoski, Spase; Stankovski, Tomislav; Stefanovska, Aneta}, Coupled nonautonomous oscillators, 163-197 [Zbl 1311.37072] \textit{Enciso, Germán A.}, Multisite mechanisms for ultrasensitivity in signal transduction, 199-224 [Zbl 1311.37073] \textit{Koch, Gilbert; Schropp, Johannes}, Mathematical concepts in pharmacokinetics and pharmacodynamics with application to tumor growth, 225-250 [Zbl 1311.37076] \textit{Herrmann, Eva; Asai, Yusuke}, Viral kinetic modeling of chronic hepatitis C and B infection, 251-268 [Zbl 1311.37074] \textit{Surulescu, Christina; Surulescu, Nicolae}, Some classes of stochastic differential equations as an alternative modeling approach to biomedical problems, 269-307 [Zbl 1311.37039]