Abstract
We are concerned with the cyclic predator-prey systems of Volterra-Lotka type where the 1st species feeds on the 2nd, the 2nd on the 3rd, …, then-th on the 1st cyclically and each species has the self-limiting terms. The purpose of this paper is to give a necessary and sufficient condition for the parameters of this type of systems so that every nonnegative solution remains bounded as the time passes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. A. Coppel, A survey of quadratic systems. J. Differential Equations,2 (1966), 293–304.
F. R. Gantmacher, The Theory of Matrices II, Chelsea, New York, 1956.
A. N. Kolmogorov, Sulla teoria di Volterra della lotta per l’esistenza. Giorn. Ist. Ital. Attuari,7 (1936), 74–80.
N. Krikorian, The Volterra model for three species predator-prey systems: boundedness and stability. J. Math. Biol.,7 (1979), 117–132.
A. Lotka, Elements of Mathematical Biology, Dover, New York, 1956.
Y. Takeuchi, N. Adachi and H. Tokumaru, Global stability of ecosystems of the generalized Volterra type. Math. Biosci.,42 (1978), 119–136.
V. Volterra, Leçons sur la Théorie Mathématique de la Lutte pour la Vie. Gauthier-Villars, Paris, 1931.
Author information
Authors and Affiliations
Additional information
(Dedicated to the Memory of Masaru Morinaka)
About this article
Cite this article
Oshime, Y. Global boundedness of cyclic predator-prey systems with self-limiting terms. Japan J. Appl. Math. 5, 153–172 (1988). https://doi.org/10.1007/BF03167870
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03167870