Discrete Dynamical Systems: With Applications in Biology -2nd Edition | Book Publisher International

 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

Chemical Engineering Processes Stability Theory | Chapter 7 | Challenges and Advances in Chemical Science Vol. 1

 It is presented a theoretical analysis of the stability of non-equilibrium chemical engineering processes. A unified approach is proposed for the development of mathematical models of systems that allow for the determination of the velocities at which the systems move to their thermodynamic equilibriums and their application to mathematical analysis of system velocities stability. Mathematical stability theory, evolution (autonomous) equations, bifurcation theory (stable focuses, stable cycles), parameter eigenvalues, and eigenfunctions are used for this purpose.

Author (s) Details

Dr. Christo Boyadjiev
Institute of Chemical Engineering, Bulgarian Academy of Sciences, Bulgaria, Balkans.

View Book :- https://stm.bookpi.org/CACS-V1/article/view/1796

Discrete Dynamical Systems: With Applications in Biology | Book Publisher International

 

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