A time-delay model for the effect of toxicant in a single species growth with stage-structure

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 4, 2010, Pages 2376-2389

  Agarwal, Manju ^a   Devi, Sapna ^a  

^a UNIVERSITY OF LUCKNOW   (India)

Author keywords

Equilibria; Numerical simulation; Periodic perturbation; Stability; Stage structure; Time delay; Toxicants

Indexed keywords

BOUNDEDNESS; CONSTANT-EMISSIONS; EQUILIBRIA; EQUILIBRIUM DENSITY; GLOBALLY ASYMPTOTICALLY STABLE; GROWTH MODELS; MATURATION TIME; MODEL EQUATIONS; NONLINEAR DIFFERENTIAL EQUATION; NUMERICAL SIMULATION; PERIODIC PERTURBATION; POSITIVE EQUILIBRIUM; SINGLE SPECIES; TIME DELAY MODEL; TOXICANTS;

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PERIODIC STRUCTURES; TIME DELAY;

COMPUTER SIMULATION;

EID: 77955771236     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.07.011     Document Type: Article

References (20)

1. J.T. de Luna, and T.G. Hallam Effects of toxicants on population: A qualitative approach IV. Resource-consumer toxicant models Ecol. Model 35 1987 249 273
2. T.G. Hallam, and C.E. Clark Nonautonomous logistic equations in models of populations in a deteriorating environment J. Theoret. Biol. 93 1982 303 311
3. T.G. Hallam, C.E. Clarke, and G.S. Jordan Effects of toxicants on populations: A qualitative approach II, First order Kinetics J. Math. Biol. 18 1983 25 37
4. T.G. Hallam, C.E. Clark, and R.R. Lassiter Effects of toxicants on populations: A qualitative approach I. Equilibrium environmental exposure Ecol. Model 18 1983 291 304
5. H.I. Freedman, and J.B. Shukla Models for the effect of toxicant in single species and predator-prey systems J. Math. Biol. 30 1991 15 30
6. J.B. Shukla, and B. Dubey Simultaneous effects of two toxicants on biological species: A mathematical model J. Biol. Syst. 4 1996 109 130
7. J.B. Shukla, A.K. Agarwal, B. Dubey, and P. Sinha Existence and survival of two competing species in a polluted environment: A mathematical model J. Biol. Systems 9 2 2001 89 103
8. P.D.N. Shrinivasu Control environmental pollution to conserve a population Nonlinear Anal. RWA 3 2002 397 411
9. D.M. Thomas, T.W. Snell, and S.M. Joffer A control problem in polluted environment Math. Biosci. 133 1996 139 163
10. B. Buonomo, Di Liddo, and I. Sgura A diffusive convective model for the dynamics of populationtoxicant interactions: Some analytical and numerical results Math. Biosci. 157 1999 37 64
11. J.V. Bruckner, 1981, Differences in sensitivity of children and adults to chemical toxicity: The NAS panel report, Regulatory toxicology and pharmacology
12. W.G. Aiello, and H.I. Freedman A time-delay model of single species growth with stage-structure Math. Biosci. 101 1990 139 153
13. J.A. Cui, and X.Y. Song Permanence of a predator-prey system with stage-structure Discrete Contin. Dyn. Syst. Ser. B 4 3 2004 747 758
14. H.I. Freedman, and K. Gopalasamy Goblal stability in time-delayed single-species dynamics Bull. Math. Biol. 48 1986 485
15. S.A. Gourley, and Y. Kuang Wavefronts and global stability in a time-delayed population model with stage structure Proc. R. Soc. Lond. A. 459 2003 1563 1579
16. Z. Gui, and W. Ge The effect of harvesting on a predator pre system with stage-structure Ecol. Model. 187 2005 329 340
17. W.S.C. Gurney, R.M. Nisbet, and S.P. Blythe The systematic formulation of models of stage-structured populations The Dynamics of Physiologically Structured Populations (Amsterdom, 1983) Lecture Notes in Biomath. vol. 68 1986 Springer Berlin 474 494
18. R.M. Nisbet, W.S.C. Gurney, W.W. Murdoch, and McCauley Structured population models: A tool for linking effects at the individual and population level Biol. J. of the Linnean Society 37 1989 79 99
19. W. Wang, G. Mulone, V. Salemi, and V. Salone Permanence and stability of a stage-structured predator-prey model J. Math. Anal. Appl. 262 2 2001 499 528
20. H.I. Freedman The implicit function theorem in the scalar case Canad. Math. Bull. 12 1969 721 732