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)
Extinction and permanence of chemostat model with pulsed input in a polluted environment. (English) Zbl 1221.37209
Summary: A chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find the microorganism eradication periodic solution is globally asymptotically stable if some conditions are needed. At the same time we can find the condition of the nutrient and microorganism are permanent.

MSC:
37N25Dynamical systems in biology
34D05Asymptotic stability of ODE
92D25Population dynamics (general)
34D20Stability of ODE
WorldCat.org
Full Text: DOI
References:
[1] Hale, J. K.; Somolinos, A. S.: Competition for fluctuating nutrient, J math biol 18, 225-280 (1983) · Zbl 0525.92024 · doi:10.1007/BF00276091
[2] Hsu, S. B.: A competition model for a seasonally fluctuating nutrient, J math biol 18, 115-132 (1980) · Zbl 0431.92027 · doi:10.1007/BF00275917
[3] Smith, H. L.: Competitive coexistence in an oscillating chemostat, SIAM J appl math 18, 498-522 (1981) · Zbl 0467.92018 · doi:10.1137/0140042
[4] Rehim, Hehbuba; Teng, Zhidong: Permanence, average persistence and extinction in non-autonomous single-species growth chemostat models, Adv complex syst 9, No. 1 -- 2, 41-58 (2006) · Zbl 1107.92055 · doi:10.1142/S0219525906000616
[5] Zhang, H.; Chen, L. S.; Georgescu, Paul: Impulsive control strategies for pest management, J biol syst 15, 235-260 (2007) · Zbl 1279.92058
[6] Wang, L.; Wolkowicz, Gail S. K.: A delayed chemostat with general nonmonotone response functions and differential removal rates, J math anal appl 321, 452-468 (2006) · Zbl 1092.92048 · doi:10.1016/j.jmaa.2005.08.014
[7] Yuan, S. L.; Han, M.: Bifurcation analysis of a chemostat model with two distributed delays, Chaos soliton and fract 20, 995-1004 (2004) · Zbl 1059.34059 · doi:10.1016/j.chaos.2003.09.048
[8] Butler, G. J.; Hsu, S. B.; Waltman, P.: A mathematical model of the chemostat with periodic washout rate, SLAM J appl math 45, 435-449 (1985) · Zbl 0584.92027 · doi:10.1137/0145025
[9] Lenas, P.; Pavlous, S.: Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate, Math biosci 129, 111-142 (1995) · Zbl 0828.92028 · doi:10.1016/0025-5564(94)00056-6
[10] Pilyugin, S. S.; Waltman, P.: Competition in the unstirred chemostat with periodic input and washout, SIAM J appl math 59, 1157-1177 (1999) · Zbl 0991.92035 · doi:10.1137/S0036139997323954
[11] Gakkhar, Sunita; Sahani, Saroj Kumar: A model for delayed effect of toxicant on resource-biomass system, Chaos soliton fract (2007) · Zbl 1197.34111
[12] Yang, X. F.; Jin, Z.; Xue, Y. K.: Weak average persistence and extinction of a predator -- prey system in a polluted environment with impulsive toxicant input, Chaos soliton fract 31, 726-735 (2007) · Zbl 1133.92032 · doi:10.1016/j.chaos.2005.10.042
[13] Liu, B.; Chen, L. S.; Zhang, Y. J.: The effects of impulsive toxicant input on a population in a polluted environment, J biol syst 11, 265-274 (2003) · Zbl 1041.92044 · doi:10.1142/S0218339003000907
[14] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[15] Bainov DD, Simeonov PS. Impulsive differential equations: periodic solutions and applications. Pitman monographs and surveys in pure and applied mathematics; 1993.