In Chapter 1 we studied the stability properties of first-order difference equations. In this chapter we will develop the theory for k-dimensional systems of first-order difference equations. As shown in Chapter 3, this study includes difference equations of any order. Here we are interested in the qualitative behavior of solutions without actually computing them. Realizing that most of the problems that arise in practice are nonlinear and mostly unsolvable, this investigation is of vital importance to scientists, engineers, and applied mathematicians.
KeywordsEquilibrium Point Unit Circle Stability Theory Zero Solution Positive Definite Symmetric Matrix
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