以下为句子列表：
英文: Abstract: In the paper, bifurcation phenomena of one kind of reaction-diffusion equations are investigated. Used singularity theory based on the method of L-S(Liapunov-Schmidt), satisfactory results are obtained.
中文: 文摘:文章讨论了一类反应扩散方程的分歧(分岔)现象.运用所谓基于L-S(李雅普诺夫-施密特)约化的奇异理论方法,得到了满意的结果.
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英文: According to the bifurcation diagram, the effects of parameters disturbance on system performance are discussed, and the sufficient condition of occurring border collision bifurcation is given.
中文: 借助分岔图讨论稳定区域附近参数变化对系统特性的影响，给出边界碰撞分岔产生的条件。
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英文: Based on the recent situation and trend of the nonlinear systems, we present some recent developments and important problems in stochastic dynamics such as response, bifurcation, chaos, synchronization and control.
中文: 摘要介绍了非线性随机动力学的响应、分岔、混沌以及混沌同步与控制的研究现状和发展趋势，探讨了随机复动力系统、时滞系统、逼近方法和数值方法研究中的若干问题及其进展。
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英文: By virtue of the stochastic bifurcation theory,the transition of the atom movement at a crack tip in fatigue damage system is investigated.Using the singular point theory of one-dimensional diffusion process and the stochastic averaging approach of energy
中文: 采用随机分叉理论，探讨疲劳损伤系统裂尖粒子运动性质突变.利用一维扩散过程的奇点理论，并结合能量包络的随机平均法，建立了随机扰动的疲劳损伤同宿分叉系统裂尖粒子运动模型,通过研究奇异边界的扩散指数、漂移指数以及特征指数特性，考查疲劳损伤裂尖粒子运动的同宿分叉系统受参激白噪声影响的分叉行为.
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英文: Firstly, negotiation can improve the communication and deepen the understanding between the two parties, which helps them reach an agreement on the basis of dissolving the contradiction and bifurcation, and thus cooperate successfully or make a deal.
中文: 首先，谈判可以促进双方的沟通，加深相互的了解，有助于双方解除矛盾分歧达成共识，从而成功合作或者做成生意。
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