A note on asymptotic behaviors of stochastic population model with Allee effect

Applied Mathematical Modelling

Volumn 35, Issue 9, 2011, Pages 4611-4619

  Yang, Qingshan ^a   Jiang, Daqing ^a  

^a NORTHEAST NORMAL UNIVERSITY   (China)

Author keywords

Allee effect; Asymptotic stability; Feller's test; It 's formula

Indexed keywords

ALLEE EFFECT; ASYMPTOTIC BEHAVIORS; FELLER'S TEST; NUMERICAL SIMULATION; STOCHASTIC POPULATION MODELS;

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 79955575035     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2011.03.034     Document Type: Article

References (16)

1. Liebhold A.M., MacDonald W.L.D., Bergdahl D., Mastro V. Invasion by exotic forest pests: a threat to forest ecosystems. For. Sci. Mon. 1995, 30:1-49.
2. Vitousek P.M., D'Antonio C.M., Loope L.L., Westbrooks R. Biological invasions as global environmental change. Am. Scientist 1996, 84:468-478.
3. Parker I.M., Simberloff D.S., Lonsdale W.M., Goodell M., Wonham P.M., Kareiva P.M., Williamson M.H., VonHolle B., Moyle P.B., Byers J.E., Goldwasser L. Impact: toward a framework for understanding the ecological effects of invaders. Biol. Invasions 1999, 1:3-19.
4. Simberloff D.S., Mack R.N., Lonsdale W.M., Evans H.F., Clout M., Bazzaz F.A. Biotic Invasions: Causes, Epidemiology, Global Consequences and Control. Issues in Ecology 2000, vol. 5. Ecological Society of America, Washington, DC.
5. Lande R. Risks of population extinction from demographic and environmental stochasticity and random catastrophes. Am. Nat. 1993, 142:911-927.
6. Nee S. How populations persist?. Nature 1994, 367:123-124.
7. Stephens P.A., Sutherland W.J. Consequences of the Allee effect for behavior ecology and conservation. Trends. Ecol. Evol. 1999, 14:401-405.
8. Allee W.C. Animal Aggregations, A Study in General Sociology 1931, University of Chicago Press, Chicago.
9. Keitt T.H., Lewis M.A., Holt R.D., Effects Allee Invasion pinning, and species borders. Am. Nat. 2001, 157(2):203-216.
10. Holt R.D., Keitt T.H., Lewis M.A., Maurer B.A., Taper M.L. Theoretical models of species' borders: single species approaches. OIKOS 2005, 108:18-27.
11. Ackleh A., Allen L., Carter J. establishing a beachhead: a stochastic population model with an Allee effect applied to species invation. Theor. Popul. Biol. 2007, 71:290-300.
12. Mao X., Marion G., Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Process. Appl. 2002, 97:95-110.
13. Krstić M., Jovanović M. On stochastic population model with the Allee effect. Math. Comput. Model. 2010, 52:370-379.
14. Xiping S., Yongji W. Stability analysis of a stochastic logistic model with nonlinear diffusion term. Appl. Math. Model. 2008, 32:2067-2075.
15. Karatzas I., Shreve S. Brownian Motion and Stochastic Calculus 1988, Springer Verlag, New York.
16. Kloeden E.P., Platen E. Numerical Solution of Stochastic Differential Equations 1992, Springer Verlag, Berlin.