Relative position of limit cycles in an immune responsec

Dynamical Systems

Volumn 21, Issue 3, 2006, Pages 351-361

  Zhu, L ^a   Huang, X ^a  

^a Yangzhou Polytechnic University   (China)

Author keywords

[No Author keywords available]

Indexed keywords

IMMUNE RESPONSE; LIMIT CYCLES; PHASE PLANE;

ANTIBODIES; ANTIGENS; MATHEMATICAL MODELS; VECTORS;

IMMUNOLOGY;

EID: 33749490487     PISSN: 14689367     EISSN: 14689375     Source Type: Journal    
DOI: 10.1080/14689360600565938     Document Type: Article

References (15)

1. Bell, G.I., 1973, Predator-prey equations simulating an immune response. Mathematical Biosciences, 16, 291-314.
2. Pimbley Jr, G.H., 1974, Periodic solutions of predator-prey equations simulating an immune response. Mathematical Biosciences, 21, 251-277.
3. Pimbley Jr, G.H., 1976, Periodic solutions of third order predator-prey equations simulating an immune response. Archive for Rational Mechanics and Analysis, 64, 169-192.
4. Pimbley Jr, G.H., 1976, Bifurcation behavior of periodic solutions of the third order simulated immune response problem. Archive for Rational Mechanics and Analysis, 64, 169-192.
5. Hsu, I.D. and Kazarinnoff, N.D., 1977, Existence and stability of periodic solutions of a third order nonlinear autonomous system simulating immune response in animals. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 77, 163-175.
6. Huang, X., 1991, Uniqueness of limit cycles in a predator-prey model simulating an immune response. International Journal of Systems Science, 22, 579-585.
7. Cui, Q. and Lawson, G.J., 1982, Study on models of single populations: an expansion of the logistic and exponential equations. Journal of Theoretical Biology, 98, 645-659.
8. Merrill, S.J., 1980, In: T.A. Burton (Ed.), Modeling and Differential Equations in Biology (New York: Marcel Dekker).
9. Kuang, Y., 1988, On the location and period of limit cycles in Cause-type predator-prey system. Journal of Mathematical Analysis and Applications, 142, 130-143.
10. Jilek, M. and Prilkrylova, D., 1985, In: G.W. Hoffman and T. Hraba (Eds), Immunology and Epidemiology (Berlin: Springer).
11. May, R.M., 1972, Limit cycles in predator-prey communities. Science, 177, 900-902.
12. Kuang, Y. and Freedman, H.I., 1988, Uniqueness of limit cycle in Cause-type models of predator-prey system. Mathematical Biosciences, 88, 67-84.
13. Huang, X.C. and Merrill, S.J., 1989, Conditions for uniqueness of limit cycles in general predator-prey system. Mathematical Biosciences, 96, 47-60.
14. Huang, X.C. and Zhu, L., 2005, Limit cycles in a general Kolmogorov model. Nonlinear Analysis: Theory, Methods and Applications, 60(8), 1393-1414.
15. Pilyugin, S.S. and Waltman, P., 2003, Multiple limit cycles in the chemostat with variable yield. Mathematical Biosciences, 182, 151-166.