Exactly Solvable Models of Biological Invasion

 INTRODUCTION
Why exactly solvable models are important
Intra- and inter-species interactions and local population dynamics
Basic mechanisms of species transport
Biological invasion: main facts and constituting examples
MODELS OF BIOLOGICAL INVASION
Diffusion-reaction equations
Integral-difference models
Space-discrete models
Stochastic models
Concluding remarks
BASIC METHODS AND RELEVANT EXAMPLES
The Cole-Hopf transformation and the Burgers equation as a paradigm
Further application of the Cole-Hopf transformation
Method of piecewise linear approximation
Exact solutions of a generalized Fisher equation
More about ansatz
SINGLE-SPECIES MODELS
Impact of advection and migration
Accelerating population waves
The problem of critical aggregation
DENSITY-DEPENDENT DIFFUSION
The Aronson-Newman solution and its generalization
Stratified diffusion and the Allee effect
MODELS OF INTERACTING POPULATIONS
Exact solution for a diffusive predator-prey system
Migration waves in a resource-consumer system
SOME ALTERNATIVE AND COMPLEMENTARY APPROACHES
Wave speed and the eigenvalue problem
Convergence of the initial conditions
Convergence and the paradox of linearization
Application of the comparison principle
ECOLOGICAL EXAMPLES AND APPLICATIONS
Invasion of Japanese beetle in the United States
Mount St. Helens recolonization and the impact of predation
Stratified diffusion and rapid plant invasion
APPENDIX: BASIC BACKGROUND MATHEMATICS
Ordinary differential equations and their solutions
Phase plane and stability analysis
Diffusion equation

References
Index