Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems

Abstract

In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi-homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a center in piecewise smooth quadratic quasi-homogeneous systems. Moreover, the center is global and non-isochronous if it exists, which cannot appear in smooth quadratic quasi-homogeneous systems. Then the global structures of piecewise smooth quadratic quasi-homogeneous but non-homogeneous systems are studied. Finally we investigate limit cycle bifurcations of the piecewise smooth quadratic quasi-homogeneous center and give the maximal number of limit cycles bifurcating from the periodic orbits of the center by applying the Melnikov method for piecewise smooth near-Hamiltonian systems.

Stability and bifurcation analysis of Filippov food chain system with food chain control strategy

“…Non-smooth or switched dynamical systems exhibit a wide variety of complex phenomena which cannot be explained by the classical theory. It is naturally used to model a great variety of engineering devices, as well as used in applied sciences to model a wide variety of physical systems and technological devices, for more details see [1,4,6,7,8,9,10,23,26,31,33]. The interactions among organisms and their environment, and the evolution of species are the most important biological processes in ecology and population.…”