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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 8
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Original Articles

The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment

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Pages 1143-1155 | Received 17 Mar 2009, Accepted 16 Jun 2009, Published online: 21 Sep 2010

References

  • Hallam , TG , Clark , CE and Jordan , GS . 1983 . Effects of toxicants on population: A qualitative approach, II. First order kinetics . J. Math. Biol. , 18 ( 1 ) : 25 – 37 .
  • Hallam , TG , Clark , CE and Lassiter , RR . 1983 . Effects of toxicant on population: A qualitative approach. I. Equilibrium environmental exposure . Ecol. Model. , 18 : 291 – 304 .
  • Liu , B , Chen , LS and Zhang , YJ . 2003 . The effects of impulsive toxicant input on a population in a polluted environment . J. Biol. Syst. , 11 ( 3 ) : 265 – 274 .
  • Xiao , YN and Chen , LS . 2003 . How do the spatial structure and time delay affect the persistence of a polluted species . Appl. Anal. , 82 ( 3 ) : 253 – 267 .
  • Srinivasu , PDN . 2002 . Control of environmental pollution to conserve a population . Nonlinear Anal. Real World Appl. , 3 : 397 – 411 .
  • Bainov , D and Simeonov , P . 1993 . “ Pitman Monographs and Surveys in Pure and Applied Mathematics ” . In Impulsive Differential Equations: Periodic Solutions and Applications , Vol. 66 , New York : Longman Scientific .
  • Lakshmikantham , V , Bainov , D and Simeonov , P . 1989 . Theory of Impulsive Differential Equations , Singapore : World Scientific .
  • Liu , B , Chen , LS and Zhang , YJ . 2005 . The dynamics of a prey-dependent consumption model concerning impulsive control strategy . Appl. Math. Comput. , 169 : 305 – 320 .
  • Liu , B , Zhang , YJ and Chen , LS . 2004 . Dynamic complexities of a Holling I predator–prey Model concerning periodic biological and chemical control . Chaos Solitons Fractals , 22 ( 1 ) : 123 – 134 .
  • Liu , B and Chen , LS . 2005 . Dynamic complexities in Lotka–Volterra predator–prey system concerning impulsive control strategy . Int. J. Bifurcation Chaos , 15 ( 2 ) : 517 – 531 .
  • Liu , B , Teng , ZD and Liu , WB . 2007 . Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations . Chaos Solitons Fractals , 31 ( 2 ) : 356 – 370 .
  • Meng , XZ and Chen , LS . 2008 . Permanence and global stability in an impulsive Lotka–Volterra N-Species competitive system with both discrete delays and continuous delays . Int. J. Biomath. , 1 ( 2 ) : 179 – 196 .
  • Meng , XZ and Chen , LS . 2008 . The dynamics of a new SIR epidemic model concerning pulse vaccination strategy . Appl. Math. Comput. , 197 ( 2 ) : 582 – 597 .
  • Song , XY and Xiang , ZY . 2006 . The prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects . J. Theor. Biol. , 242 ( 3 ) : 683 – 698 .
  • Song , XY , Hao , MY and Meng , XZ . 2009 . A stage-structured predator–prey model with disturbing pulse and time delays . Appl. Math. Model. , 33 ( 1 ) : 211 – 223 .
  • Tang , SY , Xiao , YN and Cheke , RA . 2008 . Multiple attractors of host C parasitoid models with integrated pest management strategies: Eradication persistence and outbreak . Theor. Population Biol. , 73 ( 2 ) : 181 – 197 .
  • Tang , SY and Cheke , RA . 2008 . Models for integrated pest control and their biological implications . Math. Biosci. , 215 ( 1 ) : 115 – 125 .
  • Jiao , JJ and Chen , LS . 2008 . Global attractivity of a stage-structure variable coefficients predator–prey system with time delay and impulsive perturbations on predators . Int. J. Biomath. , 1 ( 2 ) : 197 – 208 .
  • Zhao , Z and Song , XY . 2008 . Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate . Math. Comput. Simul. , 79 ( 3 ) : 500C510
  • Gao , SJ , Teng , ZD and Xie , DH . Analysis of a delayed SIR epidemic model with pulse vaccination . Chaos Solitons Fractals , 40(2) (2009), pp. 1004–1011
  • Meng , XZ and Chen , LS . 2008 . Permanence and global stability in an impulsive Lotka–Volterra N-species competitive system with both discrete delays and continuous delays . Int. J. Biomath. , 1 ( 2 ) : 179 – 196 .
  • Sun , S and Chen , LS . 2008 . Permanence and complexity of the eco-epidemiological model with impulsive perturbation . Int. J. Biomath. , 1 ( 2 ) : 121 – 132 .
  • Zhang , H , Georgescu , P and Chen , LS . 2008 . An impulsive predator–prey system with Beddington–Deangelis functional response and time delay . Int. J. Biomath. , 1 ( 1 ) : 1 – 17 .
  • Nie , LF , Teng , ZD , Hu , L and Peng , JG . 2009 . Existence and stability of periodic solution of a predator–prey model with state dependent impulsive effects . Math. Comput. Simul. , 74 ( 7 ) : 2122 – 2134 .
  • Tang , SY and Chen , LS . 2002 . Density-dependent birth rate, birth pulses and their population dynamic consequences . J. Math. Biol. , 44 : 185 – 199 .
  • Song , XY and GUO , HJ . 2008 . Global stability of a stage-structure predator–prey system . Int. J. Biomath. , 1 ( 3 ) : 313 – 326 .
  • Song , XY and Chen , LS . 2001 . Optimal harvesting and stability for a two competitive system with stage structure . Math. Biosci. , 170 : 173 – 186 .
  • Aiello , WG and Freedman , HI . 1990 . A time delay model of single species growth with stage structure . Math. Biosci. , 101 : 139 – 156 .
  • Tang , SY and Chen , LS . 2003 . Quasiperiodic solutions and chaos in a periodically forced predator-prey model with age structure for predator . Int. J. Bifurcation Chaos , 13 ( 4 ) : 973 – 980 .

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