If we choose r as a parameter, the dependence of F on r is complicated because renters the definition of z_t. Thus, we choose a as a parameter. It is well known that delayis the important factor to cause the differenc...If we choose r as a parameter, the dependence of F on r is complicated because renters the definition of z_t. Thus, we choose a as a parameter. It is well known that delayis the important factor to cause the differences between differential-difference and ordinarydifferential equations. So we choose the delay as a parameter for studying the bifurcationof delay differential equations. In this note, we investigate the Hopf bifurcation for展开更多
In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation....In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation. Furthermore, we analyze the local Hopf bifurcation of the modified equation with nonlinear relation about stem＇s increase, including the occurrence, the bifurcation direction, the stability and the approximation expression of the bifurcating periodic solution using the theory of normal form and center manifold. Finally, the obtained results of these two equations are compared, which finds that the result about the period of their bifurcating periodic solutions is obviously different, while the bifurcation direction and stability are identical.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘If we choose r as a parameter, the dependence of F on r is complicated because renters the definition of z_t. Thus, we choose a as a parameter. It is well known that delayis the important factor to cause the differences between differential-difference and ordinarydifferential equations. So we choose the delay as a parameter for studying the bifurcationof delay differential equations. In this note, we investigate the Hopf bifurcation for
文摘In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation. Furthermore, we analyze the local Hopf bifurcation of the modified equation with nonlinear relation about stem＇s increase, including the occurrence, the bifurcation direction, the stability and the approximation expression of the bifurcating periodic solution using the theory of normal form and center manifold. Finally, the obtained results of these two equations are compared, which finds that the result about the period of their bifurcating periodic solutions is obviously different, while the bifurcation direction and stability are identical.
