Linear and logistic models with time dependent coefficients
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Date
2016-01-11
Authors
Mir, Youness
Dubeau, Francois
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We sutdy the effects of some properties of the carrying capacity on the solution of the linear and logistic differential equations. We present results concerning the behaviour and the asymptotic behaviour of their solutions. Special attention is paid when the carrying capacity is an increasing or a decreasing positive function. For more general carrying capacity, we obtain bounds for the corresponding solution by constructing appropriate subsolution and supersolution. We also present a decomposition of the solution of the linear, and logistic, differential equation as a product of the carrying capacity and the solution to the corresponding differential equation with a constant carrying capacity.
Description
Keywords
Growth models, Linear model, Logistic model, Carrying capacity, Product decomposition
Citation
Mir, Y., & Dubeau, F. (2016). Linear and logistic models with time dependent coefficients. <i>Electronic Journal of Differential Equations, 2016</i>(18), pp. 1-17.