Discrete-time dynamical systems, also known as difference equations, are increasingly being utilised to model biological and ecological systems in which each measurement is separated by a time interval. The iterative maps are used in this modelling technique. Iterative maps are an important aspect of nonlinear systems dynamics because they allow us to fit the output of the previous iteration to the following iteration. In general, solving a system of difference equations explicitly is difficult. Different approaches to solving different types of difference equations exist. This book teaches discrete-time dynamical systems theory principles, theorems, and methods that are frequently utilised in the study and analysis of local dynamics of biological systems, as well as many conventional applications of the theory to many domains in biology. Stability theory, bifurcation theory, and chaos theory are three important aspects of discrete-time dynamical systems theory that we will study in this book. In the subject of discrete-time dynamical systems, stability theory is concerned with the stability of solutions of differential equations and orbits of dynamical systems under minor perturbations of initial circumstances. Bifurcation theory analyses changes in the qualitative behaviour or topological structure of the solutions of a family of differential equations from the perspective of dynamical systems. Finally, chaos theory is a discipline of dynamical systems that studies chaotic states of a dynamical system that is frequently regulated by deterministic laws and whose solutions exhibit irregular behaviour and are extremely sensitive to beginning conditions. As a result, this book combines three key aspects of discrete-time dynamical systems theory with their fascinating biological applications.
Author(s) Details
Tahmineh Azizi
Department of Mathematics, Kansas State University, USA.
Bacim Alali
Department of Mathematics, Kansas State University, USA.
Gabriel Kerr
Department of Mathematics, Kansas State University, USA.
View Book:- https://stm.bookpi.org/DDSABE/article/view/2813
No comments:
Post a Comment