Abstract. Based on a real root isolation algorithm for multivariate polynomial systems proposed in [1], the construction of small amplitude limit cycles for differential polynomial systems is considered. After the Liapunov constants are obtained for each system, the problem for the estimation of the number of small amplitude limit cycles bifurcated from a fine focus is changed to the following question: can we isolate the real roots for the polynomial system of the Liapunov constants? More than ten examples of Lotka-Volterra, cubic and Lienard systems are dealt with in a general way by using the real root isolation algorithm [2, 3, 4].

References

1. Lu Z., He B., Luo Y., Pan L., An algorithm of real root isolation for polynomial systems, MM-Research Preprints, Academia Sinica, 20, 187-198 (2001).
2. Lu Z., He B., Luo Y., Pan L., The construction of small amplitude limit cycles for differential polynomial systems, preprint.
3. Lu Z., Luo Y., Two limit cycles in three-dimensional Lotka-Volterra systems, Computers Math. Appl., 44, 51-66 (2002).
4. Lu Z., Luo Y., Three limit cycles for a three-dimensional Lotka-Volterra competitive system with a heteroclinic cycle, Computers Math. Appl., 46, 281-288 (2003).