Mathematical analysis of a delayed stage-structured predator-prey model with impulsive diffusion between two predators territories

Ecological Complexity

Volumn 16, Issue , 2013, Pages 59-67

  Dhar, Joydip ^a   Jatav, Kunwer Singh ^a  

^a ABV INDIAN INSTITUTE OF INFORMATION TECHNOLOGY AND MANAGEMENT   (India)

Author keywords

Extinction; Global attractivity; Impulsive diffusion; Monotone concave map; Permanence; Stroboscopic map

Indexed keywords

EID: 84887187961     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2012.08.001     Document Type: Article

References (33)

1. Aiello W.G., Freedman H.I. A time-delay model of single-species growth with stage structure. Mathematical Biosciences 1990, 101(2):139-153.
2. Bainov D., Simeonov P. Systems with Impulse Effect: Stability, Theory, and Applications 1989, Ellis Horwood, Chichester, England/New York.
3. Bainov D., Simeonov P. Impulsive Differential Equations: Periodic Solution and Applications 1993, Longman, London.
4. Beretta E., Solimano F. Global stability and periodic orbits for two patch predator-prey diffusion delay models. Mathematical Biosciences 1987, 85:153-183.
5. Chen S., Zhang J., Young T. Existence of positive periodic solution for nonautonomous predator-prey system with diffusion and time delay. Journal of Computational and Applied Mathematics 2003, 159(2):375-386.
6. Cui J., Chen L. Permanence and extinction in logistic and lotka-volterra systems with diffusion. Journal of Mathematical Analysis and Applications 2001, 258(2):512-535.
7. Cui J., Takeuchi Y., Lin Z. Permanence and extinction for dispersal population systems. Journal of Mathematical Analysis and Applications 2004, 298(1):73-93.
8. DuTemple L.A., Stone L.M. Tigers 1996, Lerner Publications.
9. Funasaki E., Kot M. Invasion and chaos in a periodically pulsed mass-action chemostat. Theoretical Population Biology 1993, 44:203-224.
10. Hui J., Chen L. A single species model with impulsive diffusion. Acta Mathematicae Applicatae Sinica-English Series 2005, 21(1):43-48.
11. Jiao J. Analysis of a predator-prey model with predators impulsively diffusing between two patches. Discrete and Continuous Dynamical Systems-Series B 2010, 14:1081-1094.
12. Jiao J. The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system. Discrete Dynamics in Nature and Society 2010.
13. Jiao J., Chen L. Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators. International Journal of Biomathematics 2008, 1(2):197-208.
14. Jiao J., Chen L., Cai S., Wang L. Dynamics of a stage-structured predator-prey model with prey impulsively diffusive between two patches. Nonlinear Analysis: Real World Applications 2010, 11:2748-2756.
15. Jiao J., Chen L., Yang X., Cai S. Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches. Mathematics and Computers in Simulation 2009, 80:522-532.
16. Jiao J., Pang G., Chen L., Luo G. A delayed stage-structured predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Applied Mathematics and Computation 2008, 195(1):316-325.
17. Kuang Y. Delay Differential Equation with Application in Population Dynamics 1987, Academic Press, New York.
18. Lakmeche A., Arino O. Bifurcation of nontrivial periodic solution of impulsive differential equations arising chemotherapeutic treatment. Dynamics of Continuous, Discrete and Impulsive Systems 2000, 7:265-287.
19. Lakshmikantham V., Bainov D.D., Simeonov P. Theory of Impulsive Differential Equations 1989, World Scientific, Singapor.
20. Levin S.A. Dispersion and population interactions. American Naturalist 1976, 108:207-228.
21. Liu X. Impulsive stabilization and applications to population growth models. Journal of Mathematics 1995, 25(1):381-395.
22. Liu X., Chen L. Complex dynamics of holling ii lotka-volterra predator-prey system with impulsive perturbations on the predator. Chaos, Solitons and Fractals 2003, 16:311-320.
23. Liu X., Zhang S. A cell population model described by impulsive pdes-existence and numerical approximation. Computers & Mathematics with Applications 1998, 36(8):1-11.
24. Liu Z., Teng Z., Zhang L. Two patches impulsive diffusion periodic single-species logistic model. International Journal of Biomathematics 2010, 3(1):127.
25. Murray, J.D., 1989. Mathematical Biology. Springer Verlag, Berlin/Heidelberg/New York.
26. Seidensticker J. Tigers 1996, MBI Publishing Company.
27. Shao Y. Analysis of a delayed predator-prey system with impulsive diffusion between two patches. Mathematical and Computer Modelling 2010, 52:120-127.
28. Shulgin B., Stone L., Agur Z. Pulse vaccination strategy in the sir epidemic model. Bulletin of Mathematical Biology 1998, 60:1-26.
29. Teng Z., Chen L. Permanence and extinction of periodic predator-prey systems in a patchy environment with delay. Nonlinear Analysis: Real World Applications 2003, 4(2):335-364.
30. Vandermeer J., Stone L., Blasius B. Categories of chaos and fractal basin boundaries in forced predator-prey models. Chaos, Solitons and Fractals 2001, 12:265-276.
31. Wang L., Liu Z., Chen L. Impulsive diffusion in single species model. Chaos, Solitons and Fractals 2007, 33(4):1213-1219.
32. Wang W., Chen L. A predator-prey system with stage-structure for predator. Computers & Mathematics with Applications 1997, 33(8):83-91.
33. Xu R., Ma Z. The effect of dispersal on the permanence of a predator-prey system with time delay. Nonlinear Analysis: Real World Applications 2008, 9(2):354-369.