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Nonoccurence of Stability Switching in Systems with Discrete Delays

Published online by Cambridge University Press:  20 November 2018

H. I. Freedman  and
K. Gopalsamy
H. I. Freedman
Affiliation:
Department of Mathematics, University of Alberta Edmonton, CanadaT6G 2G1
K. Gopalsamy
Affiliation:
Department of Mathematics, University of Alberta Edmonton, CanadaT6G 2G1
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Abstract

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A two dimensional system of differential equations with a finite number of discrete delays is considered. Conditions are derived for there to be no stability switching for arbitrary such delays.

Keywords

34K2092A17
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 52 - 58
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Blythe, S. P., Nisbet, R. M., Gurney, W. S. C. and MacDonald, N., Stability switches in distributed delay models, J. Math. Anal. Appl. 109 (1985), pp. 388–396.Google Scholar
2. Cooke, K. L., Stability of delay differential equations with applications in biology and medicine, in Mathematics in Biology and Medicine, Lecture Notes in Biomathematics No. 57, Springer-Verlag, Heidelberg (1985), pp. 439–446.Google Scholar
3. Cooke, K. L. and Grossman, Z., Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86 (1982), pp. 592–627.Google Scholar
4. Cooke, K. L. and van den Driessche, P., On zeroes of some transcendental equations, Funkcialaj Ekvacioj, Vol. 29 (1986), pp. 77–90.Google Scholar
5. Clashing, J. M., Integrodifferential equations and delay models in population dynamics, Lecture Notes in Biomathematics No. 20, Springer-Verlag, Heidelberg, 1977.10.1007/978-3-642-93073-7Google Scholar
6. Freedman, H. I., Addicott, J. F. and Rai, B., Nonobligate and obligate models of mutualism, in Population Biology Proceedings, Edmonton 1982, Lecture Notes in Biomathematics No. 52, Springer-Verlag, Heidelberg (1983), pp. 349–354.Google Scholar
7. Freedman, H. I. and Rao, V. S. H., The trade-off between mutual interference and time delays in predator-prey systems, Bull. Math. Biol. 45 (1983), pp. 991–1004.Google Scholar
8. Freedman, H. I. and Rao, V. S. H., Stability criteria for a system involving two time delays, SIAM J. Appl. Math. 46 (1986), pp. 552–560.Google Scholar
9. Gopalsamy, K., Delayed responses and stability in two-species systems, J. Austral. Math. Soc. Ser. B. 25 (1984), pp. 473–500.Google Scholar
10. Gopalsamy, K. and Aggarwala, B. D., Limit cycles in two species competition with time delays, J. Austral. Math. Soc. Ser. B. 22 (1980), pp. 148–160.Google Scholar
11. Hale, J. K., Infante, E. F. and Tsen, F.-S. P., Stability in linear delay equations, J. Math. Anal. Appl., 105 (1985), pp. 533–555.Google Scholar
12. MacDonald, N., Time lags in biological models, Lecture Notes in Biomathematics No. 27, Springer-Verlag, Heidelberg, 1978.Google Scholar
13. Mahaffy, J. M., A test for stability of linear differential-delay equations, Quart. Appl. Math. 40 (1982), pp. 193–202.Google Scholar
14. Nunney, L., The effect of long time delays in predator-prey systems, Theor. Pop. Biol. 27 (1985), pp. 202–221.Google Scholar
15. Nussbaum, R. D., Differential-delay equations with two time lags, Mem. Amer. Math. Soc. No. 205, Amer. Math. Soc., Providence, 1978.Google Scholar