Algebraic Methods in Mathematical 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 ...

Mathematical models in biology

Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable oxygen concentration. Biochemical pathways of aerotaxis remain largely elusive, however, aerotactic pattern formation is well documented. This allows mathem...

Mathematical Biology

The size, shape, and absorption coefficient of a microalgal cell determines, to a first order approximation, the rate at which light is absorbed by the cell. The rate of absorption determines the maximum amount of energy available for photosynthesis, and can be used to calculate the attenuation of light through the water column, including the effect of packaging pigments within discrete particl...