| 1. | Investigation to the periodic motions and period - doubling bifurcations of a moored ocean platform with cell - to - cell mapping method
系泊海洋平台周期运动倍周期分岔的胞映射分析 |
| 2. | Control of period - doubling bifurcation and chaos in a discrete nonlinear system by the feedback of states and parameter adjustment
状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌 |
| 3. | The effects of stochastic excitation on the period - doubling bifurcation and chaotic motions of the softening duffing oscillator , are discussed in detail
摘要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。 |
| 4. | The process from period doubling bifurcation to chaos suggests us to adjust the regulatory parameters in the system actively and scientifically , which will help the development of new system and lead the system ' s movement into the expected direction
由倍周期分岔通向混沌的道路启发人们主动地、科学地调节系统的控制参数，诱发新机制的形成，引导系统的运动朝着人们所期望的方向发展。 |
| 5. | The numerical results from the phase portraits , the period - doubling bifurcation and the poincare sections show that external stochastic excitation always masks the regular motions of a deterministic system and plays a dissipative role to the motions of the system , which causes the chaotic motions of the system to arise easily , though the period - doubling bifurcation is delayed
系统的相图、倍周期分岔图以及庞加莱映射图等方面的数值结果表明，外加随机激励的作用往往掩盖原确定性系统内在的规则运动，对原确定性系统的运动具有较典型的分散作用，可延缓系统的倍周期分岔，也可使得系统内在随机行为提前发生，即可使得系统更容易出现混沌运动。 |
| 6. | The results show that there exists such nonlinear dynamical phenomena as chaos ang quasi - period movement when the rotational speed , mass eccentric and a synthesizing parameter of the system change . from different point of view , the chaotical phenomenen induced by double period bifurcation is found . in this paper , the dynamical model of bearing - elastical rotor with a cross - section of crack is estabilished
结果表明，在这一非稳态油膜力模型下，在转速、无量纲偏心及一包含诸多因素的综合参数的变化过程中，在很大的范围内，系统运动都会出现由不断倍周期分岔导致的混沌现象和概周期运动。 |
| 7. | In the proposed three types of chaos generator belonging to this chaos family , the period - doubling - bifurcation route to chaos is observed , and in the type - in chaos generator , the torus - breakdown route to chaos is also observed . it would be a firstly observed phenomenon that the period - doubling - bifurcation route to chaos and the torus - breakdown route to chaos coexist in a same system , and it is a rarely observed phenomenon that the route of torus - breakdown to chaos can be observed in a third - order ordinary differential system
此平方混沌族中的三类模型都表现出了倍周期分岔到混沌的过程，而在第类结构中可以观察到环面破裂和倍周期分岔两种不同的通向混沌的途径，在同一个系统中可以观察到环面破裂和倍周期分岔两种不同的通向混沌的途径，相信是混沌生成研究方面的首次报道；在三阶自治系统中可以观察到环面破裂，这也是一个很少见的现象。 |
| 8. | The radiation field evolves from a steady saturation state to a limit cycle oscillation state , and eventually to chaotic oscillation state as the current increases , the region in which the field exhibits limit cycle or chaotic oscillation is called the " soft " and " hard " nonlinear regime , respectively : ( 1 ) in the " soft " nonlinear regime , the radiation field is characterized by period doubled bifurcation and the discrete power spectrum
随着电流的增大，辐射场经历由稳定饱和到极限环型的周期振荡，并最终过渡到非周期性混沌振荡的演化过程，按其状态可分为“软”和“硬”两种非线性区域： ( 1 )在“软”非线性区域，场的极限环振荡态和稳定饱和态是交替出现的，其特征是典型的倍周期分岔，输出功率谱是分立的。 |
| 9. | The author puts forward the thought of analyzing bifurcation and chaos in dc / dc converters with the theories of nonlinear dynamics , and the thought of controlling nonlinear problems with linear controlling methods of modern control theory . chapter three ( research on bifurcation and chaos in pwm dc / dc converters ) first theoretically analyzes and emulates period - doubling bifurcation of pwm dc / dc converters with the " inverse " piecewise numerical emulation . then the author analyzes in detail the sampled - data model , the mathematical model , which is suitable to the nonlinear research of dc / dc converters
第三章( pwm型dc dc变换器中分岔与混沌的研究)首先采用“逆向”分段数值仿真法对pwm型dc dc变换器中的倍周期分岔进行了理论分析与数值仿真；接着详细地分析了适合于dc dc变换器非线性研究的数学模型一采样数据模型，提出了dc dc变换器中存在环面分岔与鞍结分岔的可能性；最后通过电路实验验证了在电路参数发生变化时， dc dc变换器经历一系列的倍周期分岔通向混沌的演化过程，并对混沌态下dc dc变换器的输出特性进行了分析与小结。 |
| 10. | These research also approve some inherent phenomena in nonlinear systems such as the interleaving of stability region and instability region , the parameter sensibility of the instable modes , divergence after a relatively long time of chaotic swings ( transient chaos ) , a cascade of period double bifurcations to chaos and etc . these phenomena are of great importance to both theoretical research and engineering practice
研究还证实了一些非线性系统所特有的现象，如稳定域和不稳定域的相互交错现象，失稳模式对参数的敏感性，一段时间混沌振荡后的无界现象(称为预无界混池） ，由周期运动经一连串倍周期分岔直至混浊等。这些现象对理论研究与工程实践都具有重要意义。 |
