## An alternative formulation for a delayed logistic equation

- Date: 12/05/2006

Gail S.K. Wolkowicz (McMaster University)

University of British Columbia

After a brief review of the history and dynamics of the classical

logistic and delayed logistic equation models, an alternative

expression for a delayed logistic equation is derived 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. A complete global analysis shows

that unlike the dynamics of the classical logistic delay differential

equation model,no sustained oscillations are possible. Instead, the

dynamics of this model are more reminiscent of the classical logistic

ordinary differential equations growth model, but with some important

differences. Implications for incorporating delays in population models

are considered.

MITACS Math Biology Seminar 2006