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 Analysis: Real World Applications

Volumn 9, Issue 5, 2008, Pages 2055-2067

  Yafia, Radouane ^a   El Adnani, Fatiha ^b   Alaoui, Hamad Talibi ^b  

^a IBN ZOHR UNIVERSITY   (Morocco)

^b FACULTÉ DES SCIENCES   (Morocco)

Author keywords

Delay differential equations; Hopf bifurcation; Periodic solutions; Predator prey system; Stability unstability

Indexed keywords

BOUNDEDNESS; DELAY DIFFERENTIAL EQUATIONS; FUNCTIONAL RESPONSES; GLOBAL STABILITY; HOPF BIFURCATION; LARGE DELAYS; LIMIT CYCLING; MODEL SETS; NON-TRIVIAL EQUILIBRIUM; PERIODIC SOLUTIONS; PREDATOR-PREY MODELING; PREDATOR-PREY SYSTEM; REAL-WORLD; STABILITY/UNSTABILITY; TIME DELAYING; TYPE II;

TIME DELAY;

EID: 48349116901     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.12.017     Document Type: Article

References (12)

1. Aziz-Alaoui M.A., and Daher Okiye M. Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes. Appl. Math. Lett. 16 (2003) 1069-1075
2. Beretta E., and Kuang Y. Global analyses in some delayed ratio-depended predator-prey systems. Nonlinear Anal. Theory Methods Appl. 32 3 (1998) 381-408
3. Cooke K.L., and Grossman Z. Discrete delay, distributed delay and stability switches. J. Math. Anal. Appl. 86 (1982) 592-627
4. Cushing J.M. Integrodifferential Equations and Delay Models in Population Dynamics (1977), Springer, Heidelberg
5. Gopalsamy K. Stability on the Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic, Dordrecht
6. Hale J.K. Theory of Functional Differential Equations (1997), Springer, New York
7. Kuang Y. Delay Differential Equations, with Applications in Population Dynamics (1993), Academic Press, NewYork
8. MacDonald N. Time Lags in Biological Models (1978), Springer, Heidelberg
9. Nindjin A.F., Aziz-Alaoui M.A., and Cadivel M. Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay. Nonlinear Anal. Real World Appl. 7 5 (2006) 1104-1118
10. Upadhyay R.K., and Rai V. Crisis-limited chaotic dynamics in ecological systems. Chaos Solitons Fractals 12 2 (2001) 205-218
11. Upadhyay R.K., and Iyengar S.R.K. Effect of seasonality on the dynamics of 2 and 3 species prey-predator system. Nonlinear Anal.: RealWorld Appl. 6 (2005) 509-530
12. Xu R., and Chaplain M.A.J. Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response. Appl. Math. Comput. 130 (2002) 441-455