Limit cycles of multi-parameter polynomial dynamical systems

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, which models diabetes. By analyzing bifurcations applying Wintner–Perko termination principle, prove that such can have at most two cycles.