Centre bifurcations for a three dimensional system with quadratic terms

الملخص EN

This article is devoted to study the bifurcated periodic orbits from centre for a differential equation of third order.

Sufficient conditions for the existence of a centre are obtained by using inverse Jacobi multiplier.

As a result, we found four sets of centre conditions on the centre manifold.

For a given centre, it is shown that three periodic orbits can be bifurcated from the origin under two sets of condition and four periodic orbits under the other sets of condition.

The cyclicityes are obtained by considering the linear parts of the corresponding Liapunov quantities of the perturbed system.