General conditions for global stability in a single species population-toxicant model

Nonlinear Analysis: Real World Applications

Volumn 5, Issue 4, 2004, Pages 749-762

  Buonomo, B ^a   Lacitignola, Deborah ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

Compound matrices; Global stability; Population dynamics; Toxicants

Indexed keywords

EID: 3042649195     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2004.05.002     Document Type: Article

References (24)

1. Buonomo B. Di Liddo A. Sgura I. A diffusive-convective model for the dynamics of population-toxicant interactions: some analytical and numerical results Math. Biosci. 157 1999 37-64
2. Dubey B. Hussain J. Modelling the interaction of two biological species in a polluted environment J. Math. Anal. Appl. 246 2000 58-79
3. Fan M. Li M.Y. Wang K. Global stability of an SEIS epidemic model with recruitment and a varying total population size Math. Biosci. 170 2001 199-208
4. Fergola P. Buonomo B. Ruggieri C. Chemostat type equations modelling a polluted environment Math. Comput. Modelling 24 2 1996 13-22
5. Fergola P. Tenneriello C. Ma Z. Wen X. Effects of toxicant on chemostat models Trappl T. Cybernetics and Systems'94, Wien 1994 887-894 World Scientific Singapore
6. Fergola P. Tenneriello C. Wang W. Chemostat equations for a polluted environment with delayed nutrient recycling Chen L. Ruan S. Zhu J. Proceedings of the International Conference on Mathematical Biology, Hangzhou, May 1997 1998 41-46 World Scientific Singapore
7. Freedman H.I. Ruan S. Tang M. Uniform persistence and flows near a closed positively invariant set J. Differential Equations 6 4 1994 583-600
8. Freedman H.I. Shukla J.B. Models for the effect of toxicant in single-species and predator-prey systems J. Math. Biol. 30 1991 15-30
9. Gard T.G. A stochastic model for the effects of toxicants on populations Ecol. Modelling 51 1990 273-280
10. Guckenheimer J. Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields 1983 Springer Berlin
11. Hallam T.G. Clark C.E. Jordan G.S. Effect of toxicants on populations: a qualitative approach, II. First order kinetics J. Math. Biol. 18 1983 25-37
12. Hallam T.G. De Luna J.T. Effect of toxicants on populations: a qualitative approach, III. Environmental and food chain pathways J. Theor. Biol. 109 1984 411-429
13. Hutson V. Schmitt K. Permanence and the dynamics of biological systems Math. Biosci. 111 1992 1-71
14. Li M.Y. Graef J.R. Wang L. Karsai J. Global stability of a SEIR model with varying total population size Math. Biosci. 160 1999 191-213
15. Li M.Y. Muldowney J.S. On Bendixson's criterion J. Differential Equations 106 1993 27-39
16. Li M.Y. Muldowney J.S. Global stability of the SEIR model in epidemiology Math. Biosci. 125 1995 155-164
17. Li M.Y. Muldowney J.S. A geometric approach to global-stability problems SIAM J. Math. Anal. 27 4 1996 1070-1083
18. Liu H. Ma Z. The threshold of survival for system of two species in a polluted environment J. Math. Biol. 30 1991 49-61
19. Ma Z. Cui G. Wang W. Persistence and extinction of a population in a polluted environment Math. Biosci. 101 1990 75-97
20. Martin R.H. Jr. Logarithmic norms and projections applied to linear differential systems J. Math. Anal. Appl. 45 1974 432-454
21. Muldowney J.S. Compound matrices and ordinary differential equations Rocky Mount. J. Math. 20 1990 857-872
22. Smith R.A. An index theorem and Bendixon's negative criterion for certain differential equations of higher dimensions Proc. Roy. Soc. Edinburgh 91A 1981 63-77
23. Srinivasu P.D.N. Control of environmental pollution to conserve a population Nonlinear Anal. 3 2002 397-411
24. Wang L. Li M.Y. Kirschner D. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression Math. Biosci. 179 2002 207-217