Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

Abstract

Library of Congress Cataloging-in-Publication Data Smith, Hal L. Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems / Hal L. Smith. p. cm.-(Mathematical surveys and monographs, ISSN 0076-5376; v. 41) Includes bibliographical references and index. ISBN 0-8218-0393-X 1. Differentiable dynamical systems. 2. Monotonic functions. I. Title. II. Series: Mathematical surveys and monographs; no. 41. QA614.8.S63 1995 515 / .352-dc20 94-48032 CIP AMS softcover ISBN 978-0-8218-4487-8 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given.

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

“…As a consequence, due to the contradiction, (17) cannot have solution with non-negative real part, and the equilibrium is locally stable. The proof on global stability is essentially based method of contracting rectangles (in our case: intervals) [6,22], and in it we shall use the function g(z) = B ψ (μ)P (z). Since p(C) is decreasing, it is p(C(t)) ≤ p(0) and as a consequence:…”

Structural instability in an autophosphorylating kinase switch

“…The reader is referred, for example, for the very impressive and useful work of Feinberg et al (Craciun et al, 2006) or of Sontag and his collaborators Angeli et al, 2006;) (much of it based on the theory of monotone dynamical systems (Smith, 1995) and graph-theoretical methods; see, for example (Angeli et al, 2006)). …”

Perverse Consequences of Infrequently Culling a Pest

“…Theorem 5.2.1 on page 81 of Smith [23] immediately yields that N (t) ≥ 0 for all t > 0. For the existence of t 0 , assume for contradiction that…”

“…Since b (·) > 0 a comparison theorem is applicable and it then follows from Theorem 5.2.1 on page 81 of Smith [23] that w(t) ≥ 0 for t ≥ 0 and therefore in particular that…”