This is an overview of our recent works on the global bifurcation analysis multi-parameter polynomial dynamical systems. In particular, using bifurcation-geometric approach, we study dynamics and solve problem maximum number distribution limit cycles in a Euler–Lagrange–Liénard-type mechanical system. We also consider rational endocrine system by carrying out reduced planar quartic Topp system,...

In this paper, we show that perturbing a simple 3-d quadratic system with a center-type singular point can yield at least 10 small-amplitude limit cycles around a singular point. This result improves the 7 limit cycles obtained recently in a simple 3-d quadratic system around a Hopf singular point. Compared with Bautin’s result for quadratic planar vector fields, which can only have 3 small-amp...

This paper presents a study on the limit cycles of Zq -equivariant polynomial vector fields with degree 3 or 4. Previous studies have shown that when q = 2, cubic-order systems can have 12 small amplitude limit cycles. In this paper, particular attention is focused on the cases of q 3. It is shown that for cubicorder systems, when q = 3 there exist 3 small limit cycles and 1 big limit cycle; wh...