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Discrete Dynamical Systems (Hardcover, 2007)
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Discrete Dynamical Systems (Hardcover, 2007)
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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.
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