DETERMINATION OF LIMIT-CYCLES FOR 2-DIMENSIONAL DYNAMICAL-SYSTEMS

We consider in this paper two-dimensional dynamical systems of the form x=P(x,y),y=Q(x,y), where P and Q are analytic functions. We introduce a method for finding the limit cycles of the system. This method consists of searching for a power series solution of the equation P(partial derivative V/partial derivative x)+Q(partial derivative V/partial derivative y)=[(partial derivative P/partial derivative x)+(partial derivative Q/partial derivative y)]V. The limit cycles are determined from the condition V(x,y)=0.