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Stable oscillations in single species growth models with hereditary effects

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.

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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.

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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.
Funding AgencyGrant Number
Army Research Office (ARO)DAHC-34-68-C-006
Issue or Number:3-4
Record Number:CaltechAUTHORS:20200113-135742701
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100688
Deposited By: Tony Diaz
Deposited On:13 Jan 2020 23:43
Last Modified:16 Nov 2021 17:56

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