| 1. | Parameter region for existence of solitons in generalized kdv equation
方程孤子解的存在参数区 |
| 2. | The results show that the nonlinear instability of system can appear in certain parameter region
表明了在一定的条件下，系统将出现非线性不稳定，这构成了论文的第二章。 |
| 3. | The results obtained by the dissertation show that there exist the chaotic motions in some parameter regions . the research contents and the major results obtained in this dissertation are as follows
本文研究了倒立摆系统的非线性动力学，表明倒立摆系统在某些参数区域内可以出现分叉和混沌运动。 |
| 4. | By using qualitative theory of ordinary differential equations , we have analyzed the equilibrium points , obtained the parameter region of the existence , uniqueness and nonexistence of limit cycle of the above system
应用常微分方程定性理论，对该系统的平衡点进行分析，得到了极限环存在唯一性及不存在的参数范围。 |
| 5. | The results demonstrate that the tilted phase affects not only the relative shift and the transition height rather than the turning point , but also affects the truncation parameter region when the focal switch appears
研究结果表明，相位倾斜影响了相对焦移量、相对跃变量和焦开关发生的位置，同时也影响焦开关出现时截断参数的取值范围。 |
| 6. | The nonlinear electromagnetic force may cause the large oscillations of the rotor in some parameter regions . thus , the studies on the properties of the nonlinear dynamics and the stability for the rotor - ambs system play an important role in the engineering
非线性力的作用使转子在某些参数域中产生相当大的振动，因此分析该类系统的非线性振动特性和稳定性一直是电磁轴承-转子动力学研究的重要课题。 |
| 7. | The stability and bifurcation condition of rotor system are obtained and the way to improve system stability and reduce the vibration amplitude through adjusting system parameters is indicated ; 3 ) the strong nonlinear dynamic characteristic of high - speed rotor system is studied . the movement trend of system and the effect of system parameters to dynamic characteristic are indicated . the deference of the strong / weak nonlinear system and the unique characteristic of the strong soft - nonlinear system are pointed out ; 4 ) the bifurcation behavior of nonlinear rotor system is studied and the parameter region when chaos phenomenon is appeared is obtained in bifurcation and chaos theory
研究了系统的稳定性条件和发生分岔的条件，提出了通过改变参数来提高系统稳定性和抑制振幅的方法； 3 ）运用强非线性理论研究了轻型高速转子系统在大扰动条件下的强非线性主共振和1 / 3亚谐共振的动力学特性，给出在强非线性条件下系统的运动趋势和系统参数对系统动力学特性的影响，并进一步指出强/弱非线性系统、软/硬非线性系统的区别以及强软非线性系统的独有特性。 |
| 8. | In this paper periodically perturbed hopf bifurcation to lienard equation with limited time delay is sdudied in detail . that is , the influence of small periodic perturbations on system exhibiting hopf bifurcation is sdudied . in particular , the excitation frequency and the critical natural frequency of hopf bifurcation in the cases of harmonic resonance . subharmonic resonance , ultraharmonic resonance , and ultrasubharmonic resonance is discussed . it is shown that in some parameter regions the sestyms exhibit harmonic solution bifurcation , subharmonic solution bifurcation , ultraharmonic solution bifurcation , ultrasubharmonic solution bifurcation and quasi - periodic solution
本文详细研究了具有限时滞li nard方程的周期扰动hopf分支，即在该系统经历hopf分支时，研究小周期扰动对系统的影响，特别是讨论了扰动频率与hopf分支周期解的固有频率在共振、次调和共振、超调和共振、超次调和共振的情形。 |
