Local analytic first integrals of planar analytic differential systems

•We work for the first time with analytic differential systems.•We study the local analytic integrability.•The system is the well-known Chuaʼs system.•The method can be applied to other differential systems.

We study the existence of local analytic first integrals of a class of analytic differential systems in the plane, obtained from the Chuaʼs system studied in L.O. Chua (1992, 1995), N.V. Kuznetsov et al. (2011), G.A. Leonov et al. (2012) [6], [7], [11] and [13]. The method used can be applied to other analytic differential systems.