Volume 13, Number 1, Spring 2005
THE GENERAL PHASE PLANE SOLUTION
OF THE 2D HOMOGENEOUS SYSTEM
WITH EQUAL MALTHUSIAN TERMS:
THE QUADRATIC CASE
G. R. NICKLASON
Abstract. The general solution of the phase plane equation
for a 2D system of first order, nonlinear, autonomous differential
equations of degree n ≥ 2 having equal linear Malthusian
terms is obtained. The nonlinearity in each equation is
assumed to be in the form of a homogeneous polynomial of
degree n. The quadratic system is considered specifically and
results relating to the particular case of the LotkaVolterra system
are obtained. It is shown that in certain simple cases the
LV system can be solved to give explicit representations of the
solutions x(t) and y(t) in terms of t.
(Subscribers Only)
