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)
The dynamics of a food web consisting of two preys and a harvesting predator. (English) Zbl 1142.34335
Summary: This paper investigates the dynamical behavior of an exploited system consisting of two preys and a predator which is being harvested. The existence of biological, economic and optimum equilibrium of the system is examined. The local and global stability analysis of the model has been carried out. The optimal harvesting policy for harvesting the predator species is studied. The bifurcation diagram is drawn for biologically feasible choice of parameters and the harvest parameter is chosen in the range for which optimum equilibrium also exist. It is observed that harvesting can control the chaos.

MSC:
34C23Bifurcation (ODE)
92D25Population dynamics (general)
WorldCat.org
Full Text: DOI
References:
[1] Clark, Colin W.: Mathematical bioeconomics: the optimal management of renewable resources. (1976) · Zbl 0364.90002
[2] Mesterton-Gibbons, M.: On the optimal policy for the combined harvesting of independent species. Nat res model 2, 107-132 (1987) · Zbl 0850.92071
[3] Mesterton-Gibbons, M.: On the optimal policy for the combined harvesting of predator and prey. Nat res model 3, 63-90 (1988) · Zbl 0850.92067
[4] Chaudhuri, K. S.: A bioeconomic model of harvesting of a multispecies fishery. Ecol model 32, 267-279 (1986)
[5] Chaudhuri, K. S.: Dynamic optimization of combined harvesting of two-species fishery. Ecol model 41, 17-25 (1988)
[6] Chaudhuri, K. S.; Ray, S. Saha: Bionomic exploitation of a Lotka -- Volterra prey -- predator system. Bull Calcutta math soc 83, 175-186 (1991) · Zbl 0744.34046
[7] Chaudhuri, K. S.; Ray, S. Saha: On the combined harvesting of a prey -- predator system. J biol syst 4, No. 3, 373-389 (1996)
[8] Brauer, F.; Soudack, A. C.: Stability regions and transition phenomena for harvested predator -- prey systems. J math biol 7, 319-337 (1979) · Zbl 0397.92019
[9] Brauer, F.; Soudack, A. C.: Stability regions in predator -- prey systems with constant-rate prey harvesting. J math biol 8, 55-71 (1979) · Zbl 0406.92020
[10] Dai, G.; Tang, M.: Coexistence region and global dynamics of a harvested predator -- prey system. SIAM J appl math 58, 193-210 (1998) · Zbl 0916.34034
[11] Myerscough, M. R.; Gray, B. F.; Hogarth, W. L.; Norbury, J.: An analysis of an ordinary differential equation model for a two species predator -- prey system with harvesting and stocking. J math biol 30, 389-411 (1992) · Zbl 0749.92022
[12] Xiao, D.; Ruan, S.: Bogdanov-Takens bifurcations in predator -- prey systems with constant rate harvesting. Field inst commun 21, 493-506 (1999) · Zbl 0917.34029
[13] Gakkhar, S.; Naji, R. K.: On a food web consisting of a specialist and a generalist predator. J biol syst 11, No. 4, 365-376 (2003) · Zbl 1041.92041
[14] Klebanoff, A.; Hasting, A.: Chaos in one predator two prey model: general results from bifurcation theory. Math biosci 112, 221-223 (1994) · Zbl 0802.92017
[15] Takeuchi, Y.: Global dynamical properties of Lotka -- Volterra systems. (1996) · Zbl 0844.34006
[16] Azar, C.; Holmberg, J.; Lindgren, K.: Stability analysis of harvesting in predator -- prey model. Theoret biol 174, 13-19 (1995)
[17] Kumar, S.; Srivastava, S. K.; Chingakham, P.: Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model. Appl math comput 129, 107-118 (2002) · Zbl 1017.92041
[18] Gakkhar, S.; Naji, R. K.: Existence of chaos in two-prey, one-predator system. Chaos, solitons & fractals 17, No. 4, 639-649 (2003) · Zbl 1034.92033