Isochronicity for a $$\varvec{Z_{2}}$$ Z 2 -equivariant cubic system

Abstract

This paper is concerned with the bi-isochronous centers problem for a cubic systems in \({Z}_2\)-equivariant vector field. Being based on bi-centers condition, we compute the period constants and obtain the periodic constants basis for each center condition separately of eleven conditions by symbolic computation and numerical analysis with help of the computer algebra system Mathematica. Moreover, we give the sufficient and necessary condition that investigated cubic system has a pair of isochronous centers. In terms of the result of simultaneous isochronous centers including bi-isochronous centers, it is hardly seen in published references, our result in this paper is new.