Mathematical modeling and control of population systems: Applications in biological pest control

Applied Mathematics and Computation

Volumn 200, Issue 2, 2008, Pages 557-573

  Rafikov, M ^a   Balthazar, J M ^b   von Bremen, H F ^c  

^a University of Ijui   (Brazil)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^c CALIFORNIA STATE POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Biological pest control; Kolmogorov system; Linear feedback control; Lotka Volterra system; Mathematical modeling

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL THEORY; DYNAMICAL SYSTEMS; FEEDBACK CONTROL; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING;

BIOLOGICAL PEST CONTROL; KOLMOGOROV SYSTEMS; LINEAR FEEDBACK CONTROL; LOTKA-VOLTERRA SYSTEMS; POPULATION SYSTEMS;

PEST CONTROL;

EID: 44649189400     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.11.036     Document Type: Article

References (19)

1. Van Driesche R.G., and Bellows Jr. T.S. Biological Control (1996), Chapman and Hall, New York
2. Van den Bosh R., Messenger P.S., and Gutierrez A.P. An Introduction to Biological Control (1982), Plenum Press, New York
3. Thomas M.B., and Willis A.J. Biocontrol - risky but necessary. Trends in Ecology and Evolution 13 (1998) 325-329
4. Parrella M.P., Heinz K.M., and Nunney L. Biological control through augmentative releases of natural enemies: a strategy whose time has come. American Entomologist 38 3 (1992) 172-179
5. Goh B.S. Management and Analysis of Biological Populations (1980), Elsevier Scietific Publishing Company, Amsterdam
6. Rafikov M., and M Balthazar J. Optimal pest control problem in population dynamics. Computational and Applied Mathematics 24 1 (2005) 117
7. Bryson A.E., and Ho Y. Applied Optimal Control (1975), Hemisphere Publ. Corp., Washington, DC
8. Bernstein D.S. Nonquadratic cost and nonlinear feedback control. International Journal of Robust and Nonlinear Control 3 (1993) 211-229
9. Mills N.J., and Getz W.M. Modeling the biological control of insect pest: review of host-parasitoid models. Ecological Modelling 93 (1996) 121-143
10. Gilpin M.E. Spiral chaos in a predator-prey model. American Naturalist 113 (1979) 306-308
11. Vance R. Predation and resource partitioning in one predador-two prey model community. American Naturalist 112 (1978) 797-813
12. Lotka A.J. Fluctuations in the abundance of species considered mathematically. Nature 119 (1927) 12-13 (with comment by V. Volterra)
13. Volterra V. Fluctuations in the abundance of the species considered mathematically. Nature 118 (1926) 558-560
14. Udwadia F.E., and von Bremen H.F. An efficient and stable approach for computation of Lyapunov characteristic exponents of continuous dynamical systems. Applied Mathematics and Computation 121 2-3 (2001) 219-259
15. Kolmogorov A.N. Sulla Teoria di Volterra della Lotta per lEsisttenza. Giorn Instituto Ital. Attuari 7 (1936) 74-80
16. Berryman A.A. The theoretical foundations of biological control. In: Hawkins B.A., and Cornell H.V. (Eds). Theoretical Approaches to Biological Control (2001), Cambridge University Press
17. M. Rafikov, J.M. Balthazar, On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Comunications on Nonlinear Sience and Numerical Simulations (2007), doi:10.1016/j.cnsns.2006.12.011.
18. Bryson A.E., and Ho Y. Applied Optimal Control (1975), Hemisphere Publ. Corp., Washington, DC
19. Anderson B.D.O., and Moor J.B. Optimal Control: Linear Quadratic Methods (1990), Prentice-Hall, New York