Phase Portraits of a Family of Hamiltonian Cubic Systems
Differential Equations and Dynamical Systems(2024)
摘要
While all the phase portraits of the quadratic polynomial Hamiltonian systems in the Poincaré disc were classified in 1994 (see Artés and Llibre (J Differ Equ 107: 80–95, 1994)), we are far from the classification of the phase portraits of the cubic polynomial Hamiltonian systems in the Poincaré disc. In this paper, we deal with the one-parameter family of cubic polynomial Hamiltonian systems ẋ=y-y(y^2+3x^2μ ), ẏ=x+x(x^2+3y^2μ ), where (x,y)∈ℝ^2 are the variables and μ is a real parameter. We classify in the Poincaré disc the topological phase portraits of this family of systems when the parameter μ varies, describing the bifurcations which take place.
更多查看译文
关键词
Cubic polynomial differential systems,Cubic systems,Hamiltonian cubic systems,Poincaré compactification,Topological phase portraits,Bifurcations,37C29,37D45
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要