ANZIAM  J.  47 (2006), 387-396
Guide expansions for the recursive parametric solution of polynomial dynamical systems

G. F. D. Duff
  formerly of the Department of Mathematics
  University of Toronto
R. B. Leipnik
  Mathematics Department
  University of California
  Santa Barbara
  CA 93106--3080
C. E. M. Pearce
  School of Mathematical Sciences
  The University of Adelaide
  Adelaide SA 5005

Recursive parametric series solutions are developed for polynomial ODE systems, based on expanding the system components in series of a form studied by Weiss. Individual terms involve first-order driven linear ODE systems with variable coefficients. We consider Lotka-Volterra systems as an example.
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