Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any biological system, we seek to analyse the effect of delays on the growth of populations governed by the logistic equation. In this paper, the local stability...

In this work we consider the nonlocal stationary nonlinear problem (J ∗ u)(x) − u(x) = −λu(x) + a(x)u(x) in a domain Ω, with the Dirichlet boundary condition u = 0 in R \ Ω and p > 1. The kernel J involved in the convolution (J ∗ u)(x) = RN J(x− y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed t...

We derive an alternative expression for a delayed logistic equation, assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model...