There exists period doubling bifurcation.
同时存在着倍周期分叉现象。
There exists period doubling bifurcation and chaos.
存在着倍周期分叉现象和混沌运动。
The main route to chaos for this rotor system is the period doubling bifurcation cascade.
转子系统进入混沌的主要途径是倍周期分岔。
For fixed damping and fixed excited frequency the motion of the beam under small amplitude of force is periodic, but becomes chaotic through period doubling bifurcation with increase of the force.
对固定的参数激励频率和阻尼，当参数激励幅值较小时梁的运动是周期的，但大幅值激励会使运动通过倍周期分岔变为混沌。
The instability of the unbalanced system motion may result in doubling period bifurcation, almost periodic motion and chaotic motion.
存在不平衡量时，系统失稳可能产生拟周期分岔、倍周期分岔并可能导致混沌振动。
The system could undergo the period-doubling bifurcation, saddle-note bifurcation, symmetry-breaking bifurcation and so forth to chaos, as the control parameter was set on some certain intervals.
在一定的参数区域内，系统历经倍周期分岔、鞍结分岔、对称性破缺分岔等形式通向混沌。
The results show that when only the oil film forces are applied to the rotor, there only exists the period-doubling bifurcation arising from the instability of the lubricant in the bearings.
结果表明，当只有非线性油膜力作用时，转子只存在由于油膜失稳而导致的倍周期分岔。
The existence of grazing bifurcation involved in the period-doubling bifurcation is shown clearly.
展示了这种非光滑系统在倍周期分岔通向混沌的道路中存在的擦边分岔行为。
The system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.
当系统参数变化时，该系统可经过倍周期分岔进入混沌或产生阵发性混沌。
The effects of stochastic excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator, are discussed in detail.
讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔至混沌运动的影响。
The effects of stochastic excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator, are discussed in detail.
讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔至混沌运动的影响。
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