Liénard systems for quadratic systems with invariant algebraic curves (Q662454)

The author studies the character of the friction function \(f(x)\) and the restoring force \(g(x)\) in the Liénard system \[ {dx\over dt}= y,\quad {dy\over dt}= -g(x)- f(x)y \] to which a quadratic system with an invariant second-order algebraic curve (an ellipse that is a limit cycle, a hyberbola defining two separatrix cycles, or a parabola) or fourth-order algebraic curve with an oval being a limit cycle can be reduced. Invariant curves are constructed for quadratic systems in a five-parameter canonical family, which can readily be reduced to Liénard systems.