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
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