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A delay logistic equation with variable growth rate

Cohen, Donald S. and Rosenblat, Simon (1982) A delay logistic equation with variable growth rate. SIAM Journal on Applied Mathematics, 42 (3). pp. 608-624. ISSN 0036-1399. doi:10.1137/0142043.

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A logistic equation with distributed delay is considered in the case where the growth rate oscillates sinusoidally about a positive mean value. A delay kernel is chosen which admits bifurcation of the equilibrium state into a periodic solution when the growth rate is constant. It is shown that the fluctuations in growth rate modulate the bifurcation into a quasiperiodic solution. In certain circumstances, however, it is shown that frequency locking can occur but that this is a local phenomenon which does not persist outside the immediate vicinity of the bifurcation point.

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Additional Information:© 1982 Society for Industrial and Applied Mathematics. Received by the editors April 22, 1980, and in revised form March 27, 1981. The authors are indebted to Dr. P.T. Cummings for writing the computer program used in §4, and to Dr. J.S. Richardson for help in implementing the program.
Issue or Number:3
Record Number:CaltechAUTHORS:COHsiamjam82
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12662
Deposited On:18 Dec 2008 02:38
Last Modified:08 Nov 2021 22:31

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