Using a bifurcation geometric approach, we study the global dynamics and solve problem on maximum number distribution of limit cycles in generalized Liénard polynomial dynamical system that has at least three singular points finite part plane, which are symmetric with respect to origin.

On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit cycles is presented in analogy with revolving vessel containing superfluid He 4. Within such a representation, fast varying angle is shown to be reduced to phas...

In order to define the nonlinear behaviour of a thermoacoustic system, it is important to find the regions of parameter space where limit cycles exist. Continuation methods find limit cycles numerically in the time domain, with no additional assumptions other than those used to form the governing equations. Once the limit cycles are found, these continuation methods track them as the operating ...

* Correspondence: jinyinlai@lyu. edu.cn School of Science, Linyi University, Linyi 276005, Shandong, P.R. China Full list of author information is available at the end of the article Abstract In this article, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of seventh-degree systems are investigated. With the help of computer algebra system MATHEMATIC...