New sufficient conditions for global stability of a basic model describing population growth in a polluted environment

Proceedings of Dynamic Systems and Applications

Volumn , Issue , 2003, Pages 53-57

  Buonomo, Bruno ^a   Lacitignola, Deborah ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

LYAPUNOV METHODS; POPULATION STATISTICS;

GLOBAL STABILITY ANALYSIS; POPULATION DYNAMICS; POPULATION GROWTH;

SYSTEM STABILITY;

EID: 29244466126     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (16)

1. B. Buonomo, D. Lacitignola, General conditions for global stability in a single species population-toxicant model. Submitted.
2. P. Fergola, B. Buonomo, C. Ruggieri, Chemostat type equations modelling a polluted environment. Math. Comput, Modelling, 24, n.2:13-22, 1996.
3. P. Fergola, C. Tenneriello, Z. Ma, X. Wen, Effects of toxicant on chemostat models. Cybernetics and Systems, Wien 1994, T. Trappl ed. World Scientific, Singapore, 887-894, 1994.
4. P. Fergola, C. Tenneriello, W. Wang, Chemostat equations for a polluted environment with delayed nutrient recycling. Proc. Int. Conf. on Mathematical Biology, Hangzhou, 1997. L. Chen, S. Ruan, J. Zhu eds. World Scientific, Singapore, 41-46, 1998.
5. H.I. Freedman, S. Ruan, M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Diff. Equations, 6, n.4, 583-600, 1994.
6. H.I. Freedman, J.B. Shukla, Models for the effect of toxicant in single-species and predator-prey systems. J. Math.Biol., 30:15-30, 1991.
7. T.G. Gard, A stochastic model for the effects of toxicants on populations. Ecol. Modelling, 51: 273-280, 1990.
8. T.G. Hallam, C.E. Clark, G.S. Jordan, Effect of toxicants on populations: a qualitative approach II. First order kinetics, J. Math. Biol. 18: 25-37, 1983.
9. T.G. Hallam, J.T. De Luna, Effect of toxicants on populations: a qualitative approach III. Environmental and food chain pathways. J. Theor.Biol., 109: 411-429, 1984.
10. V. Hutson, K. Schmitt, Permanence and the dynamics of biological systems. Math.Biosci., 111: 1-71, 1992.
11. M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems. SIAM J. Math. Anal., 27, n.4: 1070-1083, 1996.
12. Z. Ma, G. Cui, W. Wang, Persistence and extinction of a population in a polluted environment. Math.Biosci., 101: 75-97, 1990.
13. R.H. Martin Jr., Logarithmic norms and projections applied to linear differential systems. J.Math.Anal.Appl., 45: 432-454, 1974.
14. J.S. Muldowney, Compound matrices and ordinary differential equations. Rocky Mount. J.Math., 20: 857-872, 1990.
15. P.D.N. Srinivasu, Control of environmental pollution to conserve a population. Nonlin. Anal., 3: 397-411, 2002.
16. L. Wang, M.Y. Li, D. Kirschner, Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression. Math.Biosci., 179: 207-217, 2002.