Global dynamics and controllability of a harvested prey-predator system

Journal of Biological Systems

Volumn 9, Issue 1, 2001, Pages 67-79

  Srinivasu, P D N ^a   Ismail, Shaik ^a   Naidu, Ch Raghavendra ^b  

^a ANDHRA UNIVERSITY   (India)

^b Department of Chemistry   (India)

Author keywords

Controllability; Harvesting; Limit cycle; Prey predator system

Indexed keywords

EID: 0010735354     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339001000311     Document Type: Article

References (15)

1. Brauer F. and A. C. Soudack, Stability regions and transition phenomena for harvested predator-prey systems, J. Math. Biol. 7 (1979) pp. 319-337.
2. Brauer F. and A. C. Soudack, Stability regions in predator-prey systems with constant prey harvesting, J. Math. Biol. 8 (1979) pp. 55-71.
3. Brauer F. and A. C. Soudack, Constant-rate stocking of predator-prey systems, J. Math. Biol. 11 (1981) pp. 1-14.
4. Brauer F. and A. C. Soudack, Coexistence properties of some predator-prey systems under constant rate harvesting, J. Math. Biol. 12 (1981) pp. 101-114.
5. C. Azar, J. Holmberg and K. Lindgren, Stability analysis of harvesting in a Predator-Prey model, J. Theor. Biol. 174 (1995) pp. 13-19.
6. Clark C. W., Mathematical Bioeconomics, The Optimal Management of Renewable Resources (John Wiley, New York, 1976).
7. Freedman H. I., Deterministic Mathematical Models in Population Ecology (Marcel Dekker, New York, 1980).
8. Goh B. S., Management and Analysis of Biological Populations, Developments in Agricultural and Managed-Forest Ecology 8 (Elsevier Scientific Publishing Company, New York, 1980).
9. G. Dai and M. Tang, Coexistence region and global dynamics of a harvested predator-prey system, Siam. J. Appl. Math. 58, No. 1 (1998) pp. 193-210.
10. Holling C. S., Some characteristics of simple types of predation and parasitism, Can. Ent. 91 (1959) pp. 385-398.
11. Holling C. S., The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Entomol. Soc. Can. 45 (1965) pp. 3-60.
12. Kuang Y. and H. I. Freedman, Uniqueness of Limit Cycles in Gause-Type models of Predator-Prey Systems, Math. Biosci. 88 (1988) pp. 67-84.
13. Larkin P. A., Exploitation in a type of predator-prey relation ship, J. Fish. Res. Board Canada 23 (1966) pp. 349-356.
14. Myerscough M. R., B. F. Gray, W. L. Hogarth and J. Norbury, An analysis of an ordinary differential equation model for a two-species prey-predator system with harvesting and stocking, J. Math. Biol. 30 (1992) pp. 389-411.
15. P. J. Hudson, A. P. Dobson and D. Newborn, Prevention of population cycles by parasite removal, Science 282 (1998) pp. 2256-2258.