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- H Sedaghat
- 2008

The scalar difference equation x n+1 = f n (x n , x n−1 , · · · , x n−k) may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally using the semicon-jugate relation on a group which yields a reduction of order through the semiconjugate factorization of… (More)

- H Sedaghat
- 2009

We discuss a general method by which a higher order difference equation on a group is transformed into an equivalent triangular system of two difference equations of lower orders. This breakdown into lower order equations is based on the existence of a semiconjugate relation between the unfolding map of the difference equation and a lower dimensional… (More)

- Hassan Sedaghat
- 2010

Considering a binary operation as a ternary relation permits certain sections of the latter (which are functions) to be used in representing an abstract semigroup as a family of the self-maps of its underlying set under function composition. The idea is thus seen to be entirely similar to the way that the sections of a partial ordering under set inclusion… (More)

A piecewise smooth mapping of the three dimensional Euclidean space is derived from a discrete-time model of combat. The mathematical analysis of this mapping focuses on the effects of discontinuity caused by the defender's withdrawal strategy-a prime component of the original model. Both the asymptotic and the transient behavior are discussed, and all the… (More)

Consider the difference equation x n+1 = cx n + f (x n − x n−1) where 0 ≤ c < 1 and f is continuous on R and has a global minimum (not necessarily unique) at the origin. Sufficient conditions are given on c and f for the unique fixed point ¯ x = f (0)/(1 − c) to be globally asymptotically stable. Also, conditions under which solutions converge to ¯ x… (More)

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