Abstract
This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimensions. We give an example when delay causes instability.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cavani M. and Farkas M., Bifurcations in a Predator-Prey Model with Memory and Diffusion I: Andronov-Hopf Bifurcation, Acta Math. Hungar., 63(3), 213–229, (1994)
Cushing J. M., Integodifferential Equations and Delay Models in Population Dynamics, Lect. Notes Biomath., 20, Springer (Berlin, 1977)
Farkas M., Periodic Motions, Springer-Verlag, Applied Mathematical Sciences, 105, (1994)
Farkas M. Dynamical Models in Biology, Academic Press, New York (2001)
Jeffries C., Klee V. and van den Driessche P., Qualitative Stability of Linear Systems, Lin. Alg. and its Appl., 87, 1–48, (1987)
Kiss K. and Kovács S., Qualitative behaviour of n-dimensional ratio-dependent predator-prey systems, Appl. Math. Comput., 199(2), 535–546, (2008) doi: 10.1016/j.amc.2007.10.019
MacDonald N., Time delay in prey-predator models, II. Bifurcation theory, Math. Biosci., 33, 226–234, (1977)
Lizana M. and Marín J., On Predator-Prey System with Diffusion and Delay, Discrete and Continuous Dynamical Systems — Series B, 6(6), 1321–1338, (2006)
Prasolov V. V., Problems and Theorems in Linear Algebra, Translations of Mathematical Monographs, Vol. 134, American Mathematical Society, Providence, RI, (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is dedicated to the memory of professor Miklós Farkas, colleague and friend.
Partially supported by the National Science Foundation, Hungary (NK 63066).
Rights and permissions
About this article
Cite this article
Kiss, K., Tóth, J. n-Dimensional ratio-dependent predator-prey systems with memory. Differ Equ Dyn Syst 17, 17–35 (2009). https://doi.org/10.1007/s12591-009-0002-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12591-009-0002-1