Exactly Solvable Models of Biological Invasion

ISBN: 9780367392413 出版年：2005 页码：232 Petrovskii, Sergei V Li, Bai-Lian CRC Press

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