Stochastic hybrid delay population dynamics: Well-posed models and extinction

Journal of Biological Dynamics

Volumn 3, Issue 1, 2009, Pages 1-21

  Yuan, Chenggui ^a   Mao, Xuerong ^b   Lygeros, John ^c  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^c ETH ZURICH   (Switzerland)

Author keywords

Brownian motion; Extinction; It formula; Ultimate boundedness

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; POPULATION DYNAMICS; SPECIES EXTINCTION; STATISTICS;

EXTINCTION, BIOLOGICAL; MODELS, BIOLOGICAL; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 77954789113     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513750802020804     Document Type: Article

References (23)

1. Ahmad, A., and Rao, M. R.M., 1994. Asymptotically periodic solutions of n-competing species problem with time delay. J. Math. Anal. Appl., 186:557–571.
2. Athans, M., 1987. Command and control (c2) theory:A challenge to control science. IEEE Trans. Automat. Control, 32:286–293.
3. Bahar, A., and Mao, X., 2004. Stochastic delay Lotka-Volterra model. J. Math. Anal. Appl., 292:364–380.
4. Basak, G. K., Bisi, A., and Ghosh, M. K., 1996. Stability of a random diffusion with linear drift. J. Math. Anal. Appl., 202:604–622.
5. Bereketoglu, H., and Gyori, I., 1997. Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay. J. Math. Anal. Appl., 210:279–291.
6. Freedman, H. I., and Ruan, S., 1995. Uniform persistence in functional differential equations. J. Differential Equations, 115:173–192.
7. Gopalsamy, K., 1992. Stability and Oscillations in Delay Differential Equations of Population Dynamics, Dordrecht:Kluwer Academic.
8. He, X., and Gopalsamy, K., 1997. Persistence, attractivity, and delay in facultative mutualism. J. Math. Anal. Appl., 215:154–173.
9. Hu, J., Wu, W., and Sastry, S., 2004. Modeling subtilin production in bacillus subtilis using stochastic hybrid systems, Edited by:Alur, R., and Pappas, G., Vol. 2993, 417–431. Hybrid Systems:Computation and Control, 7th International Workshop, HSCC 2004. Springer LNCS vol
10. Kazangey, T., and Sworder, D. D., Effective federal policies for regulating residential housing. Proc. Summer Computer Simulation Conference. San diego. pp. 1120–1128.
11. Kolmanovskii, V., and Myshkis, A., 1992. Applied Theory of Functional Differential Equations, Dordrecht:Kluwer Academic Publishers.
12. Kuang, Y., 1993. Delay Differential Equations with Applications in Population Dynamics, Boston:Academic Press.
13. Kuang, Y., and Smith, H. L., 1993. Global stability for infinite delay Lotka-Volterra type systems. J. Differential Equations, 103:221–246.
14. Liptser, R. Sh., and Shiryayev, A. N., 1986. Theory of Martingales, Nauka, Moscow:Kluwer Academic Publishers. Translation of the Russian edition
15. Mao, X., 1997. Stochastic Differential Equations and Applications, Chichester:Horwood.
16. Mao, X., Lygeros, J., and Yuan, C., 2006. “ Stochastic hybrid delay population dynamics ”. In Hybrid Systems:Computation and Control, Edited by:Hespanha, J., and Tiwari, A., 436–450. Berlin:Springer-Verlag. no. 3927 in LNCS
17. Mao, X., and Yuan, C., 2006. Stochastic Differential Equations with Markovian Switching, London:Imperial College Press.
18. Mariton, M., 1990. Jump Linear Systems in Automatic Control, New York:Marcel Dekker.
19. Skorohod, A. V., 1989. Asymptotic Methods in the Theory of Stochastic Differential Equations, Providence:American Mathematical Society.
20. Sworder, D. D., and Rogers, R. O., 1983. An LQ-solution to a control problem associated with a solar thermal central receiver. IEEE Trans. Automat. Control, 28:971–978.
21. Teng, Z., and Yu, Y., 2000. Some new results of nonautomomous Lotka-Volterra competitive systems with delays. J. Math. Anal. Appl., 241:254–275.
22. Willsky, A. S., and Levy, B. C., 1979. Stochastic stability research for complex power systems DOE Contract, LIDS, MIT, Rep. ET-76-C-01-2295
23. Yuan, C., and Lygeros, J., 2006. Asymptotic stability and boundedness of delay switching diffusions. IEEE Trans. Automat. Control, 51:171–175.