This book provides an introduction to discrete dynamical systems - a
framework of analysis that is commonly used in the ?elds of biology,
demography, ecology, economics, engineering, ?nance, and physics. The
book characterizes the fundamental factors that govern the quantitative
and qualitative trajectories of a variety of deterministic, discrete
dynamical systems, providing solution methods for systems that can be
solved analytically and methods of qualitative analysis for those
systems that do not permit or necessitate an explicit solution. The
analysis focuses initially on the characterization of the factors that
govern the evolution of state variables in the elementary context of
one-dimensional, ?rst-order, linear, autonomous systems. The f- damental
insights about the forces that a?ect the evolution of these - ementary
systems are subsequently generalized, and the determinants of the
trajectories of multi-dimensional, nonlinear, higher-order, non- 1
autonomous dynamical systems are established. Chapter 1 focuses on the
analysis of the evolution of state variables in one-dimensional,
?rst-order, autonomous systems. It introduces a method of solution for
these systems, and it characterizes the traj- tory of a state variable,
in relation to a steady-state equilibrium of the system, examining the
local and global (asymptotic) stability of this steady-state
equilibrium. The ?rst part of the chapter characterizes the factors that
determine the existence, uniqueness and stability of a steady-state
equilibrium in the elementary context of one-dimensional, ?rst-order,
linear autonomous systems.
