Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: R. S. Cantrell and C. Cosner
Title: Spatial ecology via reaction-diffusion equations
Additional book information: John Wiley & Sons Ltd., Chichester, UK, 2003, 428 pp., ISBN 0-471-49301-5, $155.00

References [Enhancements On Off] (What's this?)

  • 1. G. Butler and P. Waltman, Persistence in dynamical systems, J. Diff. Eqns. 63, 1986, 255-263. MR 87k:54058
  • 2. G. Butler, H. Freedman, and P. Waltman, Uniformly Persistent systems, Proc. Amer. Math. Soc. 96, 1986, 425-430. MR 87d:58119
  • 3. R. Cantrell, C. Cosner, V. Hutson, Permanence in ecological systems with spatial heterogeneity, Proc. Royal Soc. Edinburgh 123A, 1993, 533-559. MR 94i:35096
  • 4. M. Crandall and P. Rabinowitz, Bifurcation from Simple Eigenvalues, J. Functional Analysis 8, 1971, 321-340. MR 44:5836
  • 5. J. K. Hale, Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc., Providence (1988). MR 89g:58059
  • 6. J. Hale and P. Waltman, Persistence in Infinite-Dimensional Systems, SIAM J. Math. Anal. 20, 1989, 388-395. MR 90b:58156
  • 7. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes in Math. 840, Springer-Verlag, NY, 1981. MR 83j:35084
  • 8. P. Hess and A. C. Lazer, On an abstract competition model and applications, Nonlinear Analysis T. M. A. 16 (1991), 917-940. MR 92f:92036
  • 9. M. W. Hirsch, Differential equations and convergence almost everywhere in strongly monotone semiflows, Contemp. Math. 17 (1983), 267-285. MR 84h:34095
  • 10. M. W. Hirsch and H. L. Smith, Monotone Dynamical Systems, in preparation.
  • 11. M. W. Hirsch, X.-Q. Zhao and H. L. Smith, Chain transitivity, attractivity and strong repellors for semidynamical systems, J. Dynamics and Diff. Eqns. 13, 2001, 107-131. MR 2002a:37014
  • 12. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge, 1998. MR 99h:92027
  • 13. S.-B. Hsu, H. Smith, and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc. 348 (1996), 4083-4094. MR 97d:92021
  • 14. V. Hutson, A theorem on average Liapunov functions, Monatsh. Math. 98, 1984, 267-275. MR 86c:34086
  • 15. V. Hutson and K. Schmitt, Permanence and the dynamics of biological systems, Math. Biosciences 111, 1992, 1-71. MR 93d:92003
  • 16. L. Ladyzhenskaya, Attractors for semigroups and evolution equations, Cambridge Univ. Press, Cambridge (1991). MR 92k:58040
  • 17. X. Liang and J. Jifa, Discrete infinite-dimensional type-K monotone dynamical systems and time-periodic reaction-diffusion systems, J. Diff. Eqns. 189, 2003, 318-354. MR 2004b:37176
  • 18. H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Kyoto 30 (1984), 645-673. MR 85d:35014
  • 19. R. May and W. Leonard, Nonlinear aspects of competition between three species, SIAM J. Appl. Math. 29, 1975, 243-253. MR 52:12853
  • 20. S. J. Schreiber, Criteria for $C^r$ Robust Permanence, J. Diff. Eqs. 162, 2000, 400-426. MR 2001e:92012
  • 21. P. Schuster, K. Sigmund and R. Wolff, Dynamical systems under constant organization. III: Cooperative and competitive behavior of hypercycles, J. Diff. Eqns. 32, 1979, 357-368. MR 82b:34035b
  • 22. H. L. Smith, Monotone Dynamical Systems, an introduction to the theory of competitive and cooperative systems, Math. Surveys and Monographs, 41, American Mathematical Society, Providence, RI (1995). MR 96c:34002
  • 23. H. L. Smith, Dynamics of competition, Mathematics Inspired by Biology, Springer Lecture Notes in Math. 1714 (1999), 191-240.
  • 24. H. L. Smith and H. R. Thieme, Convergence for strongly ordered preserving semiflows, SIAM J. Math. Anal., 22 (1991), 1081-1101. MR 92m:34145
  • 25. H. L. Smith and H. R. Thieme, Stable coexistence and bi-stability for competitive systems on ordered Banach Spaces, J. Diff. Eqns. 176 (2001), 195-222. MR 2002i:47084
  • 26. H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an epidemic model), SIAM J. Math. Anal. 24, 1993, 407-435. MR 94a:34055
  • 27. Y. Wang and J. Jifa, The general properties of dicrete-time competitive dynamical systems, J. Diff. Eqns. 176, 2001, 470-493. MR 2002m:37036
  • 28. X.-Q. Zhao, Dynamical Systems in Population Biology, CMS Books in Mathematics, Springer, New York, 2003.
  • 29. X.-Q. Zhao and H. L. Smith, Robust persistence for semi-dynamical systems, Proc. WCNA 2000, Nonlinear Analysis 47, 2001, 6169-6179. MR 2004c:37031

Review Information:

Reviewer: H. L. Smith
Affiliation: Arizona State University
Email: halsmith@asu.edu
Journal: Bull. Amer. Math. Soc. 41 (2004), 551-557
MSC (2000): Primary 92D25, 35K57
Published electronically: June 17, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society