The Termination Principle of Multiple Limit Cycles for the Kukles Cubic System

We carry out the global bifurcation analysis of the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. Using the Wintner–Perko termination principle of multiple limit cycles, we solve the problem on the maximum number and distribution of limit cycles in this system. Numerical experiments are done to illustrate the obtained results.
Numerical Analysis