caa a22 4500 388109092 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013123 doi S0308210500013123 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013123 He Xue-Zhong School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia Degenerate Lyapunov functionals of a well-known prey-predator model with discrete delays [Elektronische Daten] [Xue-Zhong He] It is commonly believed that, as far as stabilities are concerned, ‘small delays are negligible in some modelling processes'. However, to have an affirmative answerfor this common belief is still an open problem for many nonlinear equations. In this paper, the classical Lotka-Volterra prey-predator equation with discrete delays is considered, and, by using degenerate Lyapunov functionals method, an affirmative answer to this open problem on both local and global stabilities of the prey-predator delay equations is given. It is shown that degenerate Lyapunov functional method is a powerful tool for studying the stability of such nonlinear delay systems. A detailed and explicit procedure of constructing such functionals is provided. Furthermore, some explicit estimates on the allowable sizes of the delays are obtained. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 755-771 0308-2105 129:4<755 1999 129 PRM https://doi.org/10.1017/S0308210500013123 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013123 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- He Xue-Zhong School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 755-771 0308-2105 129:4<755 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge