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＜電子ブック＞
Global Behavior of Nonlinear Difference Equations of Higher Order with Applications / by V.L. Kocic, G. Ladas
(Mathematics and Its Applications ; 256)

版	1st ed. 1993.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1993
本文言語	英語
大きさ	XII, 228 p : online resource
著者標目	*Kocic, V.L author Ladas, G author SpringerLink (Online service)
件　名	LCSH:Difference equations LCSH:Functional equations LCSH:System theory LCSH:Control theory LCSH:Biomathematics FREE:Difference and Functional Equations FREE:Systems Theory, Control FREE:Mathematical and Computational Biology
一般注記	1. Introduction and Preliminaries -- 2 Global Stability Results -- 3 Rational Recursive Sequences -- 4 Applications -- 5 Periodic Cycles -- 6 Open Problems and Conjectures -- A The Riccati Difference Equation -- B A Generalized Contraction Principle -- C Global Behavior of Systems of Nonlinear Difference Equations -- C.1 A Discrete Epidemic Model -- C.2 A Plant-Herbivore System -- C.3 Discrete Competitive Systems -- Author Index Nonlinear difference equations of order greater than one are of paramount impor­ tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention HTTP:URL=https://doi.org/10.1007/978-94-017-1703-8

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