In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is a...A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is also given.展开更多
It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contra...It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it.展开更多
文摘In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
文摘A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is also given.
文摘It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it.
