Nonlinear difference equations of order greater than one are of paramount importance in applications. Such equations appear naturally as a discrete analogues and as numerical solutions of differential equations and delay differential equations. They have models in various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our goal in this thesis is understanding the dynamics of nonlinear difference equations to construct the basic theory of this …led. We believe that the results of this thesis are prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. Now we are going to give some examples for applications of difference equations.

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Amr Mohamed Youssef Abd-Elaty,CFTe, was graduated from Faculty of Science Cairo University. He completed his M.Sc. in Pure Mathematics and his Ph.D. degree in Pure Mathematics from Ain Shams University.He is CFTe holder and currently working as an Assistant Professor of Pure Mathematics in Community College Riyadh, King Saud University.