JOURNAL BROWSE
Search
Advanced SearchSearch Tips
PERIODIC SOLUTIONS OF A DISCRETE TIME NON-AUTONOMOUS RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CONTROL
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
PERIODIC SOLUTIONS OF A DISCRETE TIME NON-AUTONOMOUS RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CONTROL
Zeng, Zhijun;
  PDF(new window)
 Abstract
With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.
 Keywords
ratio-dependent predator-prey system;nonautonomous difference equations;periodic solution;coincidence degree;
 Language
English
 Cited by
 References
1.
R. Arditi, L. R. Ginzburg, Coupling in predator-prey dynamics: Ratio-dependence, J. Theoretical Biology 139 (1989), 311-326 crossref(new window)

2.
M. Fan and K. Wang, Periodic solutions of a discrete time nonautonomous ratiodependent predator-prey system, Math. Comput. Model 35 (2002), 951-961 crossref(new window)

3.
M. Fan, Q. Wang, and X. F. Zou, Dynamics of a nonautonomous ratio-dependent predator-prey system, Pro. Roy. Soc. Edinburgh Sect. A (2003), 97-118 crossref(new window)

4.
H. I. Freedman, Deterministic mathematical models in population ecology, Marcel Dekker, New York, 1980

5.
H. I. Freedman and R. M. Mathsen, Persistence in predator prey systems with ratiodependent predator-infiuence, Bull. Math. BioI. 55 (1993), 817-827 crossref(new window)

6.
R. E. Gaines and J. L. Mawhin, Coincidence degree and nonlinear differential equations, Springer-Verlag, Berlin, 1977

7.
B. S. Goh, Management and analysis of biological population, Elsevier Scientific, The Netherlands, 1980

8.
S. B. Hsu, T. W. Huang, and Y. Kuang, Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system, J. Math. BioI. 42 (2003), 489-506 crossref(new window)

9.
S. B. Hsu, T. W. Huang, A ratio-dependent food chain model and its applications to biological control, J. Math. BioI. 181 (2003), 55-83 crossref(new window)

10.
J. D. Murry, Mathematical biology, Springer-Verlag, New York, 1989

11.
B. Daya Reddy, Introductory functional analysis: with applications to boundary value problems and finite elements, Springer-Verlag, 1997

12.
D. S. Tian and X. W. Zeng, Existence of at least two periodic solutions of a ratiodependent predator-prey model with exploited term, Acta Math. Appl. Sin, English series 21 (2005), no. 3, 489-494 crossref(new window)

13.
Qian Wang, Meng Fan, and Ke Wang, Dynamics of a class of nonautonomous semiratio-dependent predator-prey systems with functional responses, J. Math. Anal. Appl. 278 (2003), no. 2, 443-471 crossref(new window)