Some New Observations On The Classical Logistic Equation With Heredity

    Authors

    J. I. Frankel;S. R. Choudhury

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Models; Mathematics, Applied

    Abstract

    Several new and significant observations are presented pertaining to the classical problem of single-population growth with hereditary influences. In its conventional form, the resulting equation with heredity is mathematically represented by a nonlinear Volterra integro-differential equation. In this paper, we propose a new differential formulation where the dependent variable is now defined in terms of the integral of the unknown population. This formulation allows us to develop novel analyses leading to enlightening results. Some particular findings include: the development and analysis of an integrated phase-plane; the elucidation of the exact value for the extremum of the population and several other important functional relations at that corresponding time; the development of two analytic expressions for determining the time at which the population peaks; the determination of the upper asymptote for the cumulative population; and the development of an accurate early-time solution as obtained from a Riccati equation. Additionally, we illustrate that an analytical solution, based on Taylor Series expansions, can be developed with the aid of Mathematica(TM). A pure numerical solution is offered for comparison with the analytic solution.

    Journal Title

    Applied Mathematics and Computation

    Volume

    58

    Issue/Number

    2-3

    Publication Date

    1-1-1993

    Document Type

    Article

    Language

    English

    First Page

    275

    Last Page

    308

    WOS Identifier

    WOS:A1993MA04400008

    ISSN

    0096-3003

    Share

    COinS