Cohen, Donald S. and Coutsias, Evangelos and Neu, John C. (1979) Stable oscillations in single species growth models with hereditary effects. Mathematical Biosciences, 44 (3-4). pp. 255-267. ISSN 0025-5564. doi:10.1016/0025-5564(79)90085-3. https://resolver.caltech.edu/CaltechAUTHORS:20200113-135742701
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Abstract
We study single species growth models incorporating hereditary effects. Detailed calculations are carried out for a specific model with one delay parameter T as T varies in the entire range T>0. Using perturbation and bifurcation techniques, we show that the effect of the hereditary term is that the equilibrium state, which is stable for small values of T (say T<T₁), is unstable for T₁<T<T₂, and regains its stability for large delays T>T₂. We show that for T₁<T<T₂ a stable oscillatory state, exists which bifurcates from the equilibrium state through an exchange of stability at T=T₁ and T=T₂. Numerical computations and graphs of the solutions are given for the solutions in all ranges of T.
Item Type: | Article | ||||||
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Additional Information: | © 1979 Published by Elsevier B.V. Received 31 May 1978, Revised 19 December 1978. This work was supported in part by the U.S. Army Research Office under contract DAHC-34-68-C-006 and the National Science Foundation under Grant GP-32157X2. | ||||||
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Issue or Number: | 3-4 | ||||||
DOI: | 10.1016/0025-5564(79)90085-3 | ||||||
Record Number: | CaltechAUTHORS:20200113-135742701 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200113-135742701 | ||||||
Official Citation: | Donald S. Cohen, Evangelos Coutsias, John C. Neu, Stable oscillations in single species growth models with hereditary effects, Mathematical Biosciences, Volume 44, Issues 3–4, 1979, Pages 255-267, ISSN 0025-5564, https://doi.org/10.1016/0025-5564(79)90085-3. (http://www.sciencedirect.com/science/article/pii/0025556479900853) | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 100688 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 13 Jan 2020 23:43 | ||||||
Last Modified: | 16 Nov 2021 17:56 |
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