Abstract
In this paper we will investigate a stochastic hybrid delay population dynamics (SHDPD) and show under certain conditions, the SHDPD will have global positive solution. Ultimate boundedness and extinction, two important properties in a population systems, are discussed.
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Ahmad, A., Rao, M.R.M.: Asymptotically periodic solutions of n-competing species problem with time delay. J. Math. Anal. Appl. 186, 557–571 (1994)
Athans, M.: Command and control (c2) theory: A challenge to control science. IEEE Trans. Automat. Control 32, 286–293 (1987)
Basak, G.K., Bisi, A., Ghosh, M.K.: Stability of a random diffusion with linear drift. J. Math. Anal. Appl. 202, 604–622 (1996)
Bereketoglu, H., Gyori, I.: Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay. J. Math. Anal. Appl. 210, 279–291 (1997)
Bahar, A., Mao, X.: Stochastic delay Lotka-Volterra model. J. Math. Anal. Appl. 292, 364–380 (2004)
Freedman, H.I., Ruan, S.: Uniform persistence in functional differential equations. J. Differential Equations 115, 173–192 (1995)
Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht (1992)
He, X., Gopalsamy, K.: Persistence, attractivity, and delay in facultative mutualism. J. Math. Anal. Appl. 215, 154–173 (1997)
Hu, J., Wu, W., Sastry, S.: Modeling subtilin production in bacillus subtilis using stochastic hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 417–431. Springer, Heidelberg (2004)
Kazangey, T., Sworder, D.D.: Effective federal policies for regulating residential housing. In: Proc. Summer Computer Simulation Conference, San diego, pp. 1120–1128 (1971)
Kolmanovskii, V., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht (1992)
Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)
Kuang, Y., Smith, H.L.: Global stability for infinite delay Lotka-Volterra type systems. Differential Equations 103, 221–246 (1993)
Liptser, R.S., Shiryayev, A.N.: Theory of Martingales. Kluwer Academic Publishers, Dordrecht (1989) (Translation of the Russian edition, Nauka, Moscow, 1986)
Mariton, M.: Jump Linear Systems in Automatic Control, Marcel Dekker, New York (1990)
Skorohod, A.V.: Asymptotic Methods in the Theory of Stochastic Differential Equations. American Mathematical Society, Providence (1989)
Sworder, D.D., Rogers, R.O.: An LQ-solution to a control problem associated with a solar thermal central receiver. IEEE Trans. Automat. Control 28, 971–978 (1983)
Teng, Z., Yu, Y.: Some new results of nonautomomous Lotka-Volterra competitive systems with delays. J. Math. Anal. Appl. 241, 254–275 (2000)
Willsky, A.S., Levy, B.C.: Stochastic stability research for complex power systems, DOE Contract, LIDS, MIT, Rep. ET-76-C-01-2295 (1979)
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Lygeros, J., Mao, X., Yuan, C. (2006). Stochastic Hybrid Delay Population Dynamics. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_33
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DOI: https://doi.org/10.1007/11730637_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33170-4
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