Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

V.L. Kocic, G. Ladas (Autoren)

Buch | Hardcover

228 Seiten

1993
Springer (Verlag)
978-0-7923-2286-3 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	31.5.1993
Reihe/Serie	Mathematics and Its Applications ; 256
Reihe/Serie	Mathematics and Its Applications ; 256
Zusatzinfo	XII, 228 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	0-7923-2286-X / 079232286X
ISBN-13	978-0-7923-2286-3 / 9780792322863
Zustand	Neuware