Books by Sergei V. Petrovskii

This book investigates the mathematical analysis of biological invasions. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes.

Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of the equations that describe nonlinear problems encountered in the study of invasive species spread. The authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. They also provide new insight into important issues such as the impact of the Allee effect and the impact of predation. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice.

Demonstrates the advantages and methods of obtaining exact solutions of the equations that describe nonlinear problems encountered in the study of invasive species spread. This work presents a collection of exactly solvable models. It provides insight into issues such as the impact of the Allee effect and the impact of predation.