Optimal control of non-homogenous prey-predator models during infinite and finite time intervals

Applied Mathematics and Computation

Volumn 146, Issue 2-3, 2003, Pages 495-508

  El Gohary, Awad ^a,b   Al Ruzaiza, A S ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

^b Mansoura University   (Egypt)

Author keywords

Lyapunov Bellman technique; Non homogenous; Optimal control; Prey predator model

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; GRAPH THEORY; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; POPULATION STATISTICS; PROBLEM SOLVING;

PREY-PREDATOR MODEL;

OPTIMAL CONTROL SYSTEMS;

EID: 0043192304     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00601-X     Document Type: Article

References (15)

1. Svirezhev Yu., Logofet D.O. Stability of Biological Communities. 1983;Mir Publishers, Moscow.
2. Satulovky J.E., Tome T. Stochastic lattice gas model for a predator-prey system. Phys. Rev. E. 49:1994;5073-5079.
3. El-Gohary A., Al-Ruzaiza A.S. Optimal control of equilibrium state of prey-predator model. Non-Linear Dyn. Psychol. Life Sci. 6:2002;27-36.
4. Michel Y., James S.M. Global stability for the SEIR model in epidemiology. Math. Biosci. 125:1995;155-164.
5. Schinazi R. Predator-prey and host-parasite spatial stochastic models. Ann. Appl. Prob. 7(1):1997;1-9.
6. Schinazi R. On an interacting particles system modeling an epidemic. J. Math. Biol. 34:1996;915-925.
7. Swinton J. Extinction times and phase transitions for spatially structured closed epidemics. Bull. Math. Biol. 60:1998;215-230.
8. Christophr M., Jorge X. A simple vaccination model with multiple endemic states. Math. Biosci. 164:2000;183-201.
9. El-Gohary A. Optimal control of the genital herpes epidemic. Chaos Sol. Frac. 12:2001;1817-1822.
10. Chattopadhyay J., Arino O. A predator-prey model with disease in the prey. Non-Linear Anal. 36:1999;747-766.
11. Ahmed E., Yassen M.T. On inhomogeneous prey-predator model. J. Biomath. 15(3):2000;257-260.
12. Van Boven M., Melker E., Schellekens F.P., Kretzschmar M. Waning immunity and subclinical infection in an epidemic model: implications for pertussis in the Netherlands. Math. Biosci. 164:2000;161-182.
13. Schinazi R. Strategies to control the genital herpes epidemic. Math. Biosci. 159:1999;113-121.
14. Pitchfored J., Brindley J. Intratrophic predation in simple prey-predator models. Bull. Math. Biol. 60:1998;937-953.
15. Ya Roitenberg Automatic Control. 1992;Naouka, Moscow.