Asymptotic and Analytic Approaches in Random Evolutionary Systems

Author: Dmitri Koroliouk

Publication Date: July 18, 2023

Language: English

ISBN: 9781786309112, 9781394229468

Publisher: Wiley

This book provides a comprehensive overview of various asymptotic and analytic approaches applied to the study of random evolutionary systems. It delves into typical problems using specific examples and employs constructive mathematical models of natural processes to describe the trajectories of diffusion-type processes more realistically, rather than those of the Wiener process.

The book focuses on models where particles have some free distance between two consecutive collisions. It examines two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with an intensity parameter; and the semi-Markov evolutionary system, with an arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed.

In the proposed models, the number of possible directions of evolution can be finite or infinite. This book is an essential resource for researchers and scholars interested in the application of mathematical models to natural processes and the study of random evolutionary systems.

Key Features:

• Provides a comprehensive overview of various asymptotic and analytic approaches in random evolutionary systems
• Examines models with particles having a free distance between collisions
• Investigates Markov and semi-Markov evolutionary systems
• Describes the motion of particles with a finite speed
• Essential resource for researchers and scholars in the field

Target Audience:

• Researchers in mathematical biology and physics
• Scholars interested in random evolutionary systems
• Students of advanced mathematics and physics courses
• Professionals in the field of mathematical modeling