Effects of seasonal growth on ratio dependent delayed prey predator system

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 3, 2009, Pages 850-862

  Gakkhar, Sunita ^a   Negi, Kuldeep ^a   Sahani, Saroj Kumar ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

Author keywords

Bifurcation; Chaos; Delay; Seasonality; Stability

Indexed keywords

PREDATOR PREY SYSTEMS;

BIFURCATION; CHAOTIC OSCILLATION; DELAY; PREY-PREDATOR MODELS; PREY-PREDATOR SYSTEMS; QUASIPERIODIC OSCILLATIONS; RATIO DEPENDENT; SEASONAL GROWTH; SEASONALITY; TIME-DELAYS;

HOPF BIFURCATION;

EID: 50249089563     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2007.10.013     Document Type: Article

References (14)

1. Freedman H.I. Deterministic mathematical models in population ecology (1980), Marcel Dekker, New York
2. Gopalsamy K. Stability and oscillations in delay differential equations of population dynamics (1992), Kluwer Academic, Dordrecht, Netherlands
3. May R.M. Stability and complexity in model ecosystems (1973), Princeton University Press, Princeton, NJ
4. Kuang Y. Delay differential equations with applications in population dynamics (1993), Academic Press, New York
5. Beretta E., and Kuang Y. Global analysis in some delayed ratio-dependent predator-prey systems. Nonlinear Anal TMA 32 (1998) 381-408
6. Cushing J.M. Periodic time-dependent predator-prey system. SIAM J Appl Math 32 (1977) 82-95
7. Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J Animal Ecol 44 (1975) 331-340
8. Inoue M., and Kamifukumoto H. Scenarios leading to chaos in forced Lotka-Volterra model. Prog Theor Phys 71 (1984) 930-937
9. MacDonald N. Time delay in prey-predator models. Math Biosci 28 (1976) 321-330
10. May R.M. Time delay versus stability in population models with two and three trophic levels. Ecology 4 (1973) 315-325
11. Gakkhar S., and Singh B. Prey-predator models with seasonal variations. Chaos Solitons Fract 28 (2004) 229-239
12. Rinaldi S., Muratori S., and Kuznetsov Y. Multiple attractors catastrophes and chaos in seasonally perturbed predator-prey communities. Bull Math Biol 55 (1993) 15-35
13. Song Y., and Wei J. Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system. J Math Anal Appl 301 (2005) 1-21
14. Wang W., and Ma Z. Harmless delays for uniform persistence. J Math Anal Appl 158 (1991) 256-268