A Control Theory point of view on Beverton-Holt equation in population dynamics and some of its generalizations

Applied Mathematics and Computation

Volumn 199, Issue 2, 2008, Pages 464-481

  De la Sen, M ^a   Alonso Quesada, S ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Beverton Holt equation; Control systems; Controllability; Difference equations; Stability

Indexed keywords

CONTROL SYSTEMS; CONTROLLABILITY; MATHEMATICAL MODELS; STABILITY CRITERIA;

ADDITIVE DISTURBANCES; BEVERTON-HOLT EQUATION; REFERENCE MODEL;

DIFFERENCE EQUATIONS;

EID: 42949109680     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.10.021     Document Type: Article

References (17)

1. Barrowman N.J., Myers R.A., Hilborn R., Kehler D.G., and Field C.A. The variability among populations of coho salmon in the maximum productive rate and depensation. Ecological Applications 13 3 (2003) 784-793
2. Jensen A.L. Harvest reference points for the Beverton and Holt dynamic pool model. Fisheries Research 47 (2000) 93-96
3. Holden M. Beverton and Holt revisited. Fisheries Research 24 (1995) 3-8
4. G. Stefansson, Fish 480 (stockrec) Spawning stock, Recruitment and Production, Course at the Department of Biology of the University of Iceland using data of the Marine Research Institute of Reykjavik, Iceland, November 2005.
5. Beverton R.J.H., and Holt S.J. On the dynamics of exploited fish populations. Fisheries Investigation (1957) 1
6. Kocic V.L. A note on the nonautonomous Beverton-Holt model. Journal of Difference Equations and Applications 11 4-5 (2005) 415-422
7. Cushing J.M., and Henson S.M. A periodically forced Beverton-Holt equation. Journal of Difference Equations and Applications 8 12 (2002) 1119-1120
8. Cushing J.M., and Henson S.M. Global dynamics of some periodically forced monotone difference equations. Journal of Difference Equations and Applications 7 12 (2001) 859-872
9. Elaydi S., and Sacker R.J. Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures. Journal of Difference Equations and Applications 11 4-5 (2005) 337-346
10. Elaydi S., Sacker R.J., and equations P.d. population biology and the Cushing-Henson conjectures. Mathematical Biosciences 201 1-2 (2006) 195-207
11. S. Stevic, A short proof of the Cushing-Henson conjecture, Discrete Dynamics in Nature and Society vol. 2006, Article ID 37264, 5 pages, 2006, doi:10.1155/DDNS/2006/37264.
12. Berezansky L., and Braverman E. On impulsive Beverton-Holt difference equations and their applications. Journal of Difference Equations and Applications 10 9 (2004) 851-868
13. E.M. Elabbasy, H.A. El-Metwally, E.M. Elsayed, On the difference equation X(N + 1) = AX(N) - ((BX(N))/(CX(N) - DX(N - 1))), Advances in Difference Equations, 2006, doi:10.1155/ade/2006/82579.
14. De la Sen M., and Alonso-Quesada S. Model matching via multirate sampling with fast sampled input guaranteeing the stability of the plant zeros: extensions to adaptive control. IEE Control Theory and Applications 1 1 (2007) 210-225
15. McCarthy M.A. The Allee effect, finding mates and theoretical models. Ecological Modelling 103 (1997) 99-102
16. Hui C. Carrying capacity, population equilibrium, and environment's maximal load. Ecological Modelling 192 (2006) 317-320
17. Purchase C.F., Goddard S.V., and Brown J.A. Production of anti freeze glycoproteins in cultured and wild juvenile Atlantic cod (Gadus morhua L.) in a common laboratory environment. Canadian Journal of Zoology 79 (2001) 610-615