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中文摘要：
为进一步了解一个复杂的有不稳定奇点的三维动力系统在 Hopf分岔点附近的非线性特性，采用非线性控制器，提出了相应的控制系统，使得受控系统可能发生余维一、余维二和余维三的Hopf分岔。通过严格的数学推导给出了受控系统发生分岔的参数条件，证明了可控制系统在指定区域内发生退化分岔和可调控分岔的稳定性。
英文摘要：
In order to understand the complex three-dimensional dynamical system with the unstable nodes, we propose a nonlinear controller. The corresponding controlling system makes the codimension one, two, and three Hopf bifurcations happen. The mathematical deduction demonstrates that the system can be controlled to produce the degenerate Hopf bifurcation at desired location and stability of controllable bifurcation.
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