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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 Lotka-Volterra 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.

 

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© 2005, Canadian Applied Mathematics Quarterly (CAMQ)