论文标题
3-D混蛋系统中的零HOPF分叉
Zero-Hopf bifurcation in a 3-D jerk system
论文作者
论文摘要
我们考虑由混蛋方程$ \ dddot {x} = -a \ ddot {x} + x \ dot {x}^2 -x^3 -b x + c \ dot {x} $，带有$ a，b，c \ in \ in \ mathbb {r r} $。当$ a = b = 0 $和$ c <0 $时，位于原点的平衡点是零hopf平衡。当我们说服系数的二次扰动时，我们分析了此时发生的零HOPF分叉，并证明当扰动的参数为$ 0 $时，一个，两个或三个周期性的轨道可能会出生。
We consider the 3-D system defined by the jerk equation $\dddot{x} = -a \ddot{x} + x \dot{x}^2 -x^3 -b x + c \dot{x}$, with $a, b, c\in \mathbb{R}$. When $a=b=0$ and $c < 0$ the equilibrium point localized at the origin is a zero-Hopf equilibrium. We analyse the zero-Hopf Bifurcation that occur at this point when we persuade a quadratic perturbation of the coefficients, and prove that one, two or three periodic orbits can born when the parameter of the perturbation goes to $0$.
