Generalized Stochastic Delay Lotka–Volterra Systems

REFERENCES

• Ayala , F.J. ; Gilpin , M.E. ; Ehrenfeld , J.G. Competition between species: Theoretical models and experimental tests . Theor. Popul. Biol. 1973 , 4 , 331 – 356 .
   PubMed Web of Science ®Google Scholar
• Banks , R. Growth and Diffusion Phenomena: Mathematical Framework and Applications ; Springer Verlag : Berlin , Heidelberg , 1994 .
   Google Scholar
• Bahar , A. ; Mao , X. Stochastic delay population dynamics . International J. Pure Appl. Math. 2004 , 11 , 377 – 400 .
   Google Scholar
• Bahar , A. ; Mao , X. Stochastic delay Lotka–Volterra model . J. Math. Anal. Appl. 2004 , 292 , 364 – 380 .
   Web of Science ®Google Scholar
• Bastolla , U. ; Lässig , M. ; Manrubia , S.C. ; Valleriani , A. Biodeversity in model ecosystems, I: coexistence conditions for competing species. Theor. Popul. Biol. 2005, 235, 521–530.
   Google Scholar
• Bereketoglu , H. ; Gyori , I. Global asymptotic stability in a nonautonomous Lotka–Voterra type sysytem with infinite delay . J. Math. Anal. Appl. 1997 , 210 , 279 – 291 .
   Web of Science ®Google Scholar
• Freedman , H.I. ; Ruan , S. Uniform persistence in functional differential equations . J. Differential Equations 1995 , 115 , 173 – 192 .
   Web of Science ®Google Scholar
• He , X. ; Gopalsamy , K. Persistence, attractivity, and delay in faclutative mutualism . J. Math. Anal. Appl. 1997 , 215 , 154 – 173 .
   Web of Science ®Google Scholar
• Kuang , Y. Delay Differential Equations with Applications in Population Dynamics ; Academic Press : Boston , 1993 .
   Google Scholar
• Mao , X. Stabability of Stochastic Differential Equations with Respected to Semimartingales ; Longman : London , 1991 .
   Google Scholar
• Mao , X. Exponential Stability of Stochastic Differential Equations ; Dekker : New York , 1994 .
   Google Scholar
• Mao , X. Stochastic Differential Equations and Applications ; Horwood : Chichester , 1997 .
   Google Scholar
• Mao , X. ; Marion , G. ; Renshaw , E. Environmental Bronian noise supperesses explosions in population dynamics . Stochastic Process. Appl. 2002 , 92 , 95 – 110 .
   Google Scholar
• Mao , X. ; Sabanis , S. ; Renshaw , E. Asymptotic behaviour of the stochastic Lotka–Volterra model . J. Math. Anal. Appl. 2003 , 287 , 141 – 156 .
   Web of Science ®Google Scholar
• Mao , X. ; Yuan , C. ; Zou , J. Stochastic differential delay equations of population dynamics . J. Math. Anal. Appl. 2005 , 304 , 296 – 320 .
   Web of Science ®Google Scholar
• Schley , D. ; Doncaster , C.P. ; Sluckin , T. Population models of sperm-dependent parthenogenesis . Theor. Popul. Biol. 2004 , 229 , 559 – 572 .
   Google Scholar
• Schreiber , S.J. Generalist and specialist predators that mediate permanence in ecological communities . J. Math. Biol. 1997 , 36 , 133 – 148 .
   Web of Science ®Google Scholar
• Teng , Z. ; Yu , Y. Some new results of nonautonomous Lotka–Volterra competitive systems with delays . J. Math. Anal. Appl. 2000 , 241 , 254 – 275 .
   Web of Science ®Google Scholar
• Vereecken , K.M. ; Dens , E.J. ; Van Impe , J.F. Predictive modelling of mixed microbial populations in food products: evaluation of two-species models . J. Theor. Boil. 2000 , 205 , 53 – 72 .
   PubMed Web of Science ®Google Scholar