The Influence of Demographic Stochasticity on Population Dynamics: A Mathematical Study of Noise-Induced Bistable States and Stochastic Patterns

✍ Scribed by Tommaso Biancalani (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 123
• Series: Springer Theses
• Edition: 1
• Category: Library

✦ Synopsis

The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite. With recent advances in ecology, biochemistry and genetics it is becoming increasingly clear that real systems are in fact subject to a great deal of noise. Relevant examples include social insects competing for resources, molecules undergoing chemical reactions in a cell and a pool of genomes subject to evolution. When the population size is small, novel macroscopic phenomena can arise, which can be analyzed using the theory of stochastic processes. This thesis is centered on two unsolved problems in population dynamics: the symmetry breaking observed in foraging populations and the robustness of spatial patterns. We argue that these problems can be resolved with the help of two novel concepts: noise-induced bistable states and stochastic patterns.

✦ Table of Contents

Front Matter....Pages i-xvii
Introduction....Pages 1-17
Methods....Pages 19-30
Noise-Induced Bistability....Pages 31-61
Stochastic Waves on Regular Lattices....Pages 63-82
Stochastic Waves on Complex Network....Pages 83-98
Conclusions....Pages 99-105
Back Matter....Pages 107-113

✦ Subjects

Socio- and Econophysics, Population and Evolutionary Models; Probability Theory and Stochastic Processes; Community & Population Ecology; Biophysics and Biological Physics