zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Impulsive harvesting and stocking in a Monod-Haldane functional response predator-prey system. (English) Zbl 1127.92045
Summary: A Monod-Haldane functional response predator-prey system with impulsive harvesting and stocking is proposed, where the Monod-Haldane functional response involves group defense theory. Conditions for the system to be extinct are given and permanence conditions are established via the method of comparison involving multiple Lyapunov functions. Further influences of the impulsive harvesting and stocking on the system are studied, and numerical simulations show that the system has rich dynamical behavior.

34A37Differential equations with impulses
37N25Dynamical systems in biology
91B76Environmental economics (natural resource models, harvesting, pollution, etc.)
Full Text: DOI
[1] Clark, C. W.: Mathematical bioeconomics: the optimal management of renewable resources. (1976) · Zbl 0364.90002
[2] Clark, C. W.: Bioeconomic modelling and fisheries management. (1985)
[3] Kar, T. K.; Chaudhuri, K. S.: Harvesting in a two-prey one-predator fishery: a bioeconomic model. Anz-iam j 45, 443-456 (2004) · Zbl 1052.92052
[4] Freedman, H. I.: Deterministic mathematical models in population ecology. Monogr textbooks pure appl math 57 (1980)
[5] Hsu, S. B.: On global stability of a predator -- prey system. Math biosci 39, 1-10 (1978) · Zbl 0383.92014
[6] Kooij, R. E.; Zegeling, A.: Qualitative properties of two-dimensional predator -- prey systems. Nonlinear anal 29, 693-715 (1997) · Zbl 0883.34040
[7] Kuang, Y.; Freedman, H. I.: Uniqueness of limit cycles in gause-type models of predator -- prey systems. Math biosci 88, 67-84 (1988) · Zbl 0642.92016
[8] May, R. M.: Limit cycles in predator -- prey communities. Science 177, 900-902 (1972)
[9] Mischaikow, K.; Wolkowicz, G. S.: A predator -- prey system involving group defense: a connection matrix approach. Nonlinear anal 14, 955-969 (1990) · Zbl 0724.34015
[10] Sugie, J.; Kohno, R.; Miyazaki, R.: On a predator -- prey system of Holling type. Proc am math soc 125, 2041-2050 (1997) · Zbl 0868.34023
[11] Holmes, J. C.; Bethel, W. M.: Modification of intermediate host behavior parasites. Zool J linnean soc 51, No. Suppl. 1, 123-149 (1972)
[12] Tener, J. S.: Muskoxen. (1965)
[13] Andrews, J. F.: A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol bioeng 10, 707-723 (1968)
[14] Lakshmikantham, V.; Bainov, D.; Simeonov, P.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[15] Bainov, D.; Simeonov, P.: Impulsive differential equations: periodic solutions and applications. Ptiman monogr surv pure appl math 66, 54-121 (1993)
[16] Lakmeche, A.; Arino, O.: Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynam contin discrete impuls syst 7, 265-287 (2000) · Zbl 1011.34031
[17] Zhang, S. W.; Tan, D. J.; Chen, L. S.: Chaos in periodically forced Holling type IV predator -- prey system with impulsive perturbations. Chaos, solitons & fractals 27, 980-990 (2006) · Zbl 1097.34038
[18] Zhang, S. W.; Wang, F. Y.; Chen, L. S.: A food chain model with impulsive perturbations and Holling IV functional response. Chaos, solitons & fractals 26, 855-866 (2005) · Zbl 1066.92061
[19] Liu, X. N.; Chen, L. S.: Complex dynamics of Holling type II Lotka -- Volterra predator -- prey system with impulsive perturbations on the predator. Chaos, solitons & fractals 16, 311-320 (2003) · Zbl 1085.34529
[20] Zeng, G. Z.; Chen, L. S.; Sun, L. H.: Complexity of an SIR epidemic dynamics model with impulsive vaccination control. Chaos, solitons & fractals 26, 495-505 (2005) · Zbl 1065.92050
[21] Hui, J.; Zhu, D. M.: Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects. Chaos, solitons & fractals 29, 233-251 (2006) · Zbl 1095.92067
[22] Zhang, Y. J.; Xiu, Z. L.; Chen, L. S.: Dynamic complexity of a two-prey one-predator system with impulsive effect. Chaos, solitons & fractals 26, 131-139 (2005) · Zbl 1076.34055