Prey-predator systems with delay: Hopf bifurcation and stable oscillations

Mathematical and Computer Modelling

Volumn 25, Issue 10, 1997, Pages 77-98

  Pecelli, G ^a  

^a UNIVERSITY OF MASSACHUSETTS LOWELL   (United States)

Author keywords

Hopf bifurcation; Method of averaging; Prey predator models; Symbolic computation

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPUTATION THEORY; GEOMETRY; INTEGRAL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATIONS;

DELAY DIFFERENTIAL SYSTEMS; PREY PREDATOR SYSTEMS; SYMBOLIC COMPUTATION;

MATHEMATICAL MODELS;

EID: 0031147982     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(97)00076-9     Document Type: Article

References (18)

1. P. Wangersky and W. Cunningham, Time lag in prey predator population models, Ecology 38, 136-139 (1957).
2. G.G. Ross, A difference-differential model in population dynamics, Journal of Theoretical Biology 37, 177-192 (1972).
3. A. Leung, Periodic solutions for a prey-predator differential delay equation, Journal of Differential Equations 26, 391-403 (1977).
4. S.B. Hsu, S.P. Hubbel and P. Waltman, Competing predators, S.I.A.M. Journal of Applied Mathematics 35, 617-625 (1978).
5. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, CA, (1993).
6. H. Stech, Hopf bifurcation calculations for functional differential equations, Journal of Mathematical Analysis and Applications 109, 472-491 (1985).
7. th Conference on Decision and Control, IEEE, 821-824 (1988).
8. G. Pecelli, On a delay-differential system, in Contributions to Analysis and Geometry, (Edited by D.N. Clark, G. Pecelli, and R. Sacksteder), Johns Hopkins University Press, Baltimore, MD, 259-263 (1981).
9. G. Pecelli, Formal methods in delay-differential equations, in Proceedings of ISSAC 91, ACM Press (1991).
10. G. Pecelli, Delay-Differential Equations: Symbolic Computation and the Hopf Bifurcation, Univ. of Mass. Lowell Technical Report, (1993).
11. S.-N. Chow and J. Mallett-Paret, Integral averaging and bifurcation, Journal of Differential Equations 26, 112-159 (1977).
12. J. Hale, Theory of Functional-Differential Equations, Springer-Verlag, New York, (1977).
13. J.E. Marsden and M.F. McCracken, The Hopf Bifurcation and its Applications, Springer-Verlag, New York, (1976).
14. Y. Kuang, Global stability of Gause-type predator-prey systems, Journal of Mathematical Biology 28, 463-474 (1990).
15. R. Bellman and K.L. Cooke, Differential-Difference Equations, Academic Press, New York, (1963).
16. N. Chaffee, The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential equation, Journal of Differential Equations 4, 161-179 (1968).
17. B.W. Char, K.O. Geddes, G.H. Gonnet. B.L. Leong, M.B. Monagan and S.W. Watt, MAPLE V Library Reference Manual, Springer-Verlag, New York, (1991).
18. B.W. Char, K.O. Geddes, G.H. Gonnet. B.L. Leong, M.B. Monagan and S.W. Watt, MAPLE V Language Reference Manual, Springer-Verlag, New York, (1991).