Stochastic population dynamics under regime switching

Journal of Mathematical Analysis and Applications

Volumn 334, Issue 1, 2007, Pages 69-84

  Luo, Qi ^a   Mao, Xuerong ^b  

^a NANJING UNIVERSITY OF INFORMATION SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Boundedness; Brownian motion; It 's formula; Markov chain; Stochastic differential equation

Indexed keywords

EID: 34249314701     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.12.032     Document Type: Article

References (21)

1. Anderson W.J. Continuous-Time Markov Chains (1991), Springer
2. In: Boucher D.H. (Ed). The Biology of Mutualism (1985), Groom Helm, London
3. Butler G., Freedman H.I., and Waltman P. Uniformly persistence systems. Proc. Amer. Math. Soc. 96 (1986) 425-430
4. Du N.H., Kon R., Sato K., and Takeuchi Y. Dynamical behaviour of Lotka-Volterra competition systems: Non-autonomous bistable case and the effect of telegraph noise. J. Comput. Appl. Math. 170 (2004) 399-422
5. Freedman H.I., and Ruan S. Uniform persistence in functional differential equations. J. Differential Equations 115 (1995) 173-192
6. Gilpin M.E. Predator-Prey Communities (1975), Princeton Univ. Press
7. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic, Dordrecht
8. He X., and Gopalsamy K. Persistence, attractivity, and delay in facultative mutualism. J. Math. Anal. Appl. 215 (1997) 154-173
9. Hutson V., and Schmitt K. Permanence and the dynamics of biological systems. Math. Biosci. 111 (1992) 1-71
10. Jansen W. A permanence theorem for replicator and Lotka-Volterra system. J. Math. Biol. 25 (1987) 411-422
11. Kirlinger G. Permanence of some ecological systems with several predator and one prey species. J. Math. Biol. 26 (1988) 217-232
12. Mao X. Stability of Stochastic Differential Equations with Respect to Semimartingales (1991), Longman Scientific and Technical, London
13. Mao X. Exponential Stability of Stochastic Differential Equations (1994), Marcel Dekker, New York
14. Mao X. Stochastic Differential Equations and Applications (1997), Horwood Publishing, Chichester
15. Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79 (1999) 45-67
16. Mao X., Marion G., and Renshaw E. Environmental noise suppresses explosion in population dynamics. Stochastic Process. Appl. 97 (2002) 95-110
17. Skorohod A.V. Asymptotic Methods in the Theory of Stochastic Differential Equations (1989), Amer. Math. Soc.
18. Slatkin M. The dynamics of a population in a Markovian environment. Ecology 59 (1978) 249-256
19. Takeuchi Y. Global Dynamical Properties of Lotka-Volterra Systems (1996), World Scientific
20. Takeuchi Y., Du N.H., Hieu N.T., and Sato K. Evolution of predator-prey systems described by a Lotka-Volterra equation under random environment. J. Math. Anal. Appl. 323 2 (2006) 938-957
21. Wolin C.L., and Lawlor L.R. Models of facultative mutualism: Density effects. Amer. Natural. 124 (1984) 843-862