zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Optimal harvesting and stability for a predator-prey system with stage structure. (English) Zbl 1054.34125
A predator-prey model with stage structure is considered. The prey populations are classified as immature and mature in order to model the stage structure and a time delay is used to account the time of maturity. It is also assumed that the mature prey is being harvested at a constant rate and both the mature prey and predator have nonlinear death rates. Conditions on global stability of the steady states and a threshold value for the harvesting constant are given.
MSC:
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
34K13Periodic solutions of functional differential equations
References:
[1]Aiello, W.G., Freedman, H.I. A time-delay model of single-species growth with stage structure. Math. Biosci., 101: 139–153 (1990) · Zbl 0719.92017 · doi:10.1016/0025-5564(90)90019-U
[2]Aiello, W.G., Freedman, H.I., Wu, J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math., 52(3): 855–869 (1992) · Zbl 0760.92018 · doi:10.1137/0152048
[3]Barclay, H.J., Van Den Driessche, P. A model for a single species with two life history stages and added mortality. Ecol. Model, 11: 157–166 (1980) · doi:10.1016/0304-3800(80)90081-2
[4]Bhatta Charya, D.K., Begum, S. Bionomic equilibrium of two-species system I. Math. Biosci., 135(2): 111 (1996) · Zbl 0856.92018 · doi:10.1016/0025-5564(95)00170-0
[5]Cao, Y., Fan, J., Gard, T.C. The effects of state-structured population growth model. Nonlin. Anal. Th. Meth. Appl., 16(2): 95–105 (1992) · Zbl 0777.92014 · doi:10.1016/0362-546X(92)90113-S
[6]Clark, C.W. Mathematical bioeconomics: the optimal management of renewable resources, 2nd ed. Wiley, New York, 1990
[7]Cushing, J.M. A simple model of cannibalism. Math. Biosci., 107: 47 (1991) · Zbl 0738.92015 · doi:10.1016/0025-5564(91)90071-P
[8]Diekmann, O., Nisbet, R.W., Gurney, W.S.C., van den Bosch, F. Simple mathematical models for cannibalism: a critique and a new approach. Math. Biosci., 78: 210–46 (1986) · Zbl 0587.92020 · doi:10.1016/0025-5564(86)90029-5
[9]Murray, J.D. Mathematical Biology. Biomathematics, Vol.19. Springer-Verlag, Berlin Heidelberg, 1989
[10]Song, Xinyu, Chen, Lansun. Optimal harvesting and stability for a two species competitive system with stage structure. Mathematical Biosciences, 170(2): 173–186 (2001) · Zbl 1028.34049 · doi:10.1016/S0025-5564(00)00068-7
[11]Spencer, P.H., Collie, J.S. A simple predator-prey model of exploited marine fish populations incorporating alternate prey. ICES J. Mar. Sci., 53: 615 (1994) · doi:10.1006/jmsc.1996.0082