By Saber Elaydi

A must-read for mathematicians, scientists and engineers who are looking to comprehend distinction equations and discrete dynamics

Contains the main whole and comprehenive research of the soundness of one-dimensional maps or first order distinction equations.

Has an in depth variety of functions in a number of fields from neural community to host-parasitoid structures.

Includes chapters on persevered fractions, orthogonal polynomials and asymptotics.

Lucid and obvious writing type

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**Additional info for An Introduction to Difference Equations**

**Sample text**

I) = 4 x(n)[1 - x(n)]. 3. 1). Show that: (i) For 1 < /L S 3, x* is an attracting fixed point. (ii) For /L > 3, x* is a repelling fixed point. 4. Prove that lim n ..... oo F~ (x) = ! if 0 < x < 1. 6 The Logistic Equation and Bifurcation 43 5. 6. I). Show that if x* < x < ~, then Iim n ..... oc F;(x) = x*. 6. 1, < I + -/6. 7. 6). 1, = 1+-/6. 8. 54 using a calculator or a computer. *9. 1,X leads to the same value for the Feigenbaum number 8. ) 10. 1,I(x)1 < 8 for all x E [0, I]. 11. ) 12. 7). (b) Find the values of C where y~ is attracting, repelling, or unstable.

668576 ... 669354 ... 40 1. 6692016 .... This number is called the Feigenbaum number after its discoverer, the physicist Mitchell Feigenbaum [42]. In fact, Feigenbaum made a much more remarkable discovery: The number 8 is universal and is independent of the form of the family of maps Ill" However, the number 11-00 depends on the family of functions under consideration. 22 (Feigenbaum [42] [1978]). 6692016 does not in general depend on the family of maps. 4 The Bifurcation Diagram Here the horizontal axis represents the 11- values, and the vertical axis represents higher iterates F;(x).

10)]) Economists define the equilibrium price p* of a commodity as the price at which the demand function D(n) is equal to the supply function Sen + I). 9), respectively. 11). (b) Let ms = 2, bs = 3, md = 1, and bd = 15. Find the equilibrium price p*. Then draw a stair step diagram, for p(O) = 2. 7. Continuation of Problem 6: Economists use a different stair step diagram, as we will explain in the following steps: (i) Let the x-axis represent the price pen) and the y-axis represent Sen + 1) or D(n).