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Stability for some equations of mathematical biology and monotone flows
Published online by Cambridge University Press: 17 April 2009
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The theory of monotone flows and operators is applied to study stable equilibria of autonomous cooperative systems and stable periodic solutions of periodic perturbations of these systems. The connection between analyticity and the property of asymptotic stability is established.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 201 - 207
- Copyright
- Copyright © Australian Mathematical Society 1993
References
[1]Butler, G., Freedman, H. and Waltman, P., ‘Uniformly persistent systems’, Proc. Amer.Math. Soc. 96 (1986), 425–430.CrossRefGoogle Scholar
[2]Dancer, E.N. and Hess, P., ‘Stability of fixed points for order-preserving discrete-time dynamical system’, J. Reine Agnew. Math. 419 (1991), 125–139.Google Scholar
[3]Hale, J.K., Asymptotic behavior of dissipative systems (American Mathematical Society, Providence, Rhode Island, 1988).Google Scholar
[5]Hirsch, M.W., ‘The dynamical system approach to differential equations’, Bull. Amer.Math. Soc. 11 (1984), 1–64.CrossRefGoogle Scholar
[6]Hirsh, M.W., ‘Systems of differential equations which are competitive or cooperative II. Convergence almost everywhere’, SIAM J. Math. Anal. 196 (1985), 423–439.CrossRefGoogle Scholar
[7]Krasnoselskii, M.A., Positive solutions of operator equations (Noordhoff, Groningen, 1964).Google Scholar
[8]Lefschetz, S., Differential equations: geometrical theory (Wiley-Interscience, New York, 1957).Google Scholar
[9]Pokrovskii, A.V., ‘Existence and calculation stable regimes in nonlinear systems’, Avtomat.Telemekh 4 (1986), 16–24.Google Scholar