Linear and logistic models with time dependent coefficients

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.

Keywords

• Growth models
• linear model
• logistic model
• carrying capacity
• product decomposition