Discrete-time dynamical systems or difference equations have been increasingly used to model the

biological and ecological systems for which there is time interval between each measurement. This

modeling approach is done through using the iterative maps. Iterative maps are an essential part of

nonlinear systems dynamics as they allow us to take the output of the previous state of the system

and fit it back to the next iteration. In general, it is not easy to explicitly solve a system of difference

equations. There are different methods of solving different types of difference equations. This book

introduces concepts, theorems, and methods in discreet-time dynamical systems theory which are

widely used in studying and analysis of local dynamics of biological systems and provides many

traditional applications of the theory to different fields in biology. Our focus in this book is covering

three important parts of discrete-time dynamical systems theory: Stability theory, Bifurcation theory

and Chaos theory. Mathematically speaking, stability theory in the field of discrete-time dynamical

systems deals with the stability of solutions of difference equations and of orbits of dynamical systems

under small perturbations of initial conditions. In dynamical systems point of view, bifurcation theory

addresses the changes in the qualitative behavior or topological structure of the solutions of a family

of difference equations. Finally, chaos theory is a branch of dynamical systems which focuses on the

study of chaotic states of a dynamical system which is often governed by deterministic laws and its

solutions demonstrate irregular behavior and are highly sensitive to initial conditions. Therefore, this

book is a blend of three important parts of discrete-time dynamical systems theory and their exciting

applications to biology.

**Author (s) Details**

**Tahmineh Azizi
**Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.

**Bacim Alali
**Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.

**Gabriel Kerr
**Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/259