Quadratic Isochronous centers commute
We prove that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.
Quadratic systems equivalent by domains to a linear one: global phase portraits.
Quadratic systems with a unique finite rest point.
We study phase portraits of quadratic systems with a unique finite singularity. We prove that there are 111 different phase portraits without limit cycles and that 13 of them are realizable with exactly one limit cycle. In order to finish completely our study two problems remain open: the realization of one topologically possible phase portrait, and to determine the exact number of limit cycles for a subclass of these systems.
Quadratic systems with homoclinic cycles described by quintic curves.
Quadratic vector fields with a weak focus of third order.
We study phase portraits of quadratic vector fields with a weak focus of third order at the origin. We show numerically the existence of at least 20 different global phase portraits for such vector fields coming from exactly 16 different local phase portraits available for these vector fields. Among these 20 phase portraits, 17 have no limit cycles and three have at least one limit cycle.
Qualitative analysis for a class of plane systems.
Qualitative investigation of a two-dimensional Chua system.