Mathematical methods in systems biology

Advanced mathematical methods for biology

2 The Floquet theory of the aktion potential 3 2.1 Periodic event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Tonic spikes are limit cycles . . . . . . . . . . . . . . . . . . . . . 3 2.3 Limit cycle stability . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Eigensystem of the Floquet matrix . . . . . . . . . . . . . 6 2.4 Neutral dimension and phase shifts . . . . ...

Mathematical Methods in Biology and Neurobiology

Selected mathematical and statistical methods in biology

Some specific methods with applications in biology, ecology and related natural sciences will be presented. The stress will be on less known methods with a wide potential in applications. In the first part, correspondences between two sets will be considered as a tool for investigating various connections among their elements. One of the sets is called the set of objects and another is the set ...

Dynamical Systems with Applications in Mathematical Biology

We consider an age-structured population model of erythropoiesis including a dynamical death rate for mature cells as an attempt to understand erythrocyte lifespan distribution, a feature which may have clinical significance. The model takes the form of a system of nonlinear delay differential equations representing total circulating cells, the regulatory hormone (erythropoietin) and the moving...

Lecture Notes on Mathematical Systems Biology

The first version of these notes dates back to 2005. They were originally heavily inspired by Leah Keshet’s beautiful book Mathematical Models in Biology (McGraw-Hill, 1988), and the reader will notice much material “borrowed” from there as well as other sources. In time, I changed the emphasis to be heavier on “systems biology” ideas and lighter on traditional population dynamics and ecology. ...