JOURNAL BROWSE
Search
Advanced SearchSearch Tips
DYNAMIC ANALYSIS OF A MODIFIED STOCHASTIC PREDATOR-PREY SYSTEM WITH GENERAL RATIO-DEPENDENT FUNCTIONAL RESPONSE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
DYNAMIC ANALYSIS OF A MODIFIED STOCHASTIC PREDATOR-PREY SYSTEM WITH GENERAL RATIO-DEPENDENT FUNCTIONAL RESPONSE
Yang, Yu; Zhang, Tonghua;
  PDF(new window)
 Abstract
Abstract. In this paper, we study a modified stochastic predator-prey system with general ratio-dependent functional response. We prove that the system has a unique positive solution for given positive initial value. Then we investigate the persistence and extinction of this stochastic system. At the end, we give some numerical simulations, which support our theoretical conclusions well.
 Keywords
predator-prey model;functional response;persistent;extinct;Brownian motion;
 Language
English
 Cited by
 References
1.
R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics: ratio-dependence, J. Theor. Biol. 139 (1989), no. 3, 311-326. crossref(new window)

2.
R. Arditi, L. R. Ginzburg, and H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratio-dependent predation models, Amer. Natural. 138 (1991), no. 5, 1287-1296. crossref(new window)

3.
R. Arditi and H. Saiah, Empirical evidence of the role of heterogeneity in ratio-dependent consumption, Ecology 73 (1992), no. 5, 1544-1551. crossref(new window)

4.
M. A. Aziz-Alaoui and M. D. Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett. 16 (2003), no. 7, 1069-1075. crossref(new window)

5.
A. A. Berryman, The origins and evolution of predator-prey theory, Ecology 73 (1992), no. 5, 1530-1535. crossref(new window)

6.
L. Chen and J. Chen, Nonlinear Biological Dynamical System, Science Press, Beijing, 1993.

7.
A. P. Gutierrez, Physiological basis of ratio-dependent predator-prey theory: the metabolic pool model as a paradigm, Ecology 73 (1992), no. 5, 1552-1563. crossref(new window)

8.
D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev. 43 (2001), no. 3, 525-546. crossref(new window)

9.
S. B. Hsu, T. W. Hwang, and Y. Kuang, Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system, J. Math. Biol. 42 (2001), no. 6, 489-506. crossref(new window)

10.
C. Ji, D. Jiang, and N. Shi, Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation, J. Math. Anal. Appl. 359 (2009), no. 2, 482-498. crossref(new window)

11.
N. D. Kazarinoff and P. van den Driessche, A model predator-prey system with functional response, Math. Biosci. 39 (1978), no. 1-2, 125-134. crossref(new window)

12.
F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, London, 1998.

13.
Y. Kuang and E. Beretta, Global qualitative analysis of a ratio-dependent predator-prey system, J. Math. Biol. 36 (1998), no. 4, 389-406. crossref(new window)

14.
B. Li and Y. Kuang, Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system, SIAM J. Appl. Math. 67 (2007), no. 5, 1453-1464. crossref(new window)

15.
P. S. Mandal and M. Banerjee, Stochastic persistence and stability analysis of a modified Holling-Tanner model, Math. Methods Appl. Sci. 36 (2013), no. 10, 1263-1280. crossref(new window)

16.
A. F. Nindjin, M. A. Aziz-Alaoui, and M. Cadivel, Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay, Nonlinear Anal. Real World Appl. 7 (2006), no. 5, 1104-1118. crossref(new window)

17.
L. A. Real, The kinetics of functional response, Amer. Natural. 111 (1977), no. 978, 289-300. crossref(new window)

18.
L. A. Real, Ecological determinants of functional response, Ecology 60 (1979), no. 3, 481-485. crossref(new window)

19.
X. Song and Y. Li, Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect, Nonlinear Anal. Real World Appl. 9 (2008), no. 1, 64-79. crossref(new window)

20.
D. Xiao, W. Li, and M. Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal. Appl. 324 (2006), no. 1, 14-29. crossref(new window)

21.
D. Xiao and S. Ruan, Global dynamics of a ratio-dependent predator-prey system, J. Math. Biol. 43 (2001), no. 3, 268-290. crossref(new window)

22.
R. Yafia, F. E. Adnani, and H. T. Alaoui, Limit cycle and numerical similations for small and large delays in a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Nonlinear Anal. Real World Appl. 9 (2008), no. 5, 2055-2067.