bifurcations

简明释义

英[ˌbɪfərˈkeɪʃənz]美[ˌbaɪˈfɜrkeɪʃənz]

分支

英英释义

单词用法

同义词

反义词

例句

1.In the paper the bifurcations and chaos in a class of planar D3-equivariant mapping are studied.

本文讨论了一类平面D3等变映射的分歧和混沌性质。

2.Under the loading conditions of uniaxial and slightly biaxial tension, the characteristics of material bifurcations (plane shear banding and surface wrinkling) are demonstrated.

文中揭示了在单向和弱双向加载条件下材料分叉(平面剪切带和表面皱曲)的一些特征。

3.A method to suppress bifurcations and chaotic motions is proposed.

提出一种抑制分叉和混沌的方法。

4.Then these three mythical systems are different, so those bifurcations came into being.

这样，这三神属于的神话系统是不一样的，所以发生了这些分歧。

5.The progresses in studying bifurcations and chaos of spacecraft attitude motions are surveyed.

综述了航天器姿态运动的分岔+和混沌的研究进展。

6.By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.

利用中心流形约化方法证明了霍普夫分歧解的稳定性。

7.Study on Bifurcations and Chaos of Coupled Bending and Torsional Vibration about Fans Rotor System;

应用该模型，重点研究了动、静碰摩引起的转子弯曲和扭转非线性耦合振动。

8.Finally we use obtained normal form and universal unfolding to discuss codimension 3 degenerate bifurcations of nonlinear dynamical system.

最后利用所得到的规范形和普适开折讨论了非线性动力系统的余维3退化分叉。

9.The river has several bifurcations that create beautiful islands along its path.

这条河有几个分叉，在它的路径上形成了美丽的岛屿。

10.In decision-making, bifurcations can lead to very different outcomes depending on the chosen path.

在决策中，分叉可能导致根据选择的路径出现非常不同的结果。

11.The study of bifurcations in mathematics helps us understand the stability of solutions to equations.

数学中对分叉的研究帮助我们理解方程解的稳定性。

12.The bifurcations in the road made navigation tricky for the drivers.

道路上的分叉使得司机们导航变得棘手。

13.In biology, bifurcations can refer to the branching of blood vessels or tree limbs.

在生物学中，分叉可以指血管或树枝的分支。

作文

In the realm of decision-making, we often encounter various paths that lead us in different directions. These paths can be thought of as bifurcations, where a single route divides into two distinct options. Understanding bifurcations is crucial not only in our personal lives but also in fields such as mathematics, biology, and even social sciences. Each bifurcation represents a choice, a moment where we must weigh our options and consider the consequences of each path we may take. For instance, consider a simple scenario: you are at a crossroads in your career. You have two job offers, each with its own set of benefits and challenges. The moment you decide to pursue one over the other is a classic example of a bifurcation. This decision could significantly impact your future, shaping your professional trajectory and personal satisfaction. In this context, recognizing the nature of bifurcations helps us appreciate the weight of our choices. In mathematics, bifurcations refer to points where a small change in the system's parameters causes a sudden qualitative change in its behavior. For example, in dynamical systems, a bifurcation might signify a shift from stable equilibrium to chaotic behavior. This concept is crucial for scientists and engineers who model complex systems, as it allows them to predict how changes in initial conditions can lead to vastly different outcomes. By studying bifurcations, we gain insights into the stability and transitions of systems, helping us make informed predictions about their future states. In biology, bifurcations can be observed in evolutionary processes. When species diverge from a common ancestor, they undergo bifurcations in their evolutionary paths, leading to the diversity of life we see today. Understanding these evolutionary bifurcations helps biologists trace the lineage of species and comprehend the mechanisms of natural selection. Each bifurcation in evolution illustrates how organisms adapt to their environments, emphasizing the importance of these decisions in the survival of species. Moreover, in social sciences, bifurcations can represent moments of significant change in societal norms or behaviors. For example, during major political movements, society may experience bifurcations in public opinion, where groups divide based on differing beliefs and values. Recognizing these bifurcations allows sociologists to analyze shifts in societal trends and understand the factors that drive collective behavior. In conclusion, bifurcations are pivotal moments that occur across various domains of life. They symbolize choices that can lead to entirely different outcomes, whether in personal decisions, mathematical models, biological evolution, or societal changes. By understanding bifurcations, we become more aware of the complexity of our world and the critical nature of the decisions we make. Embracing the concept of bifurcations empowers us to navigate life's challenges with greater insight, ultimately leading to more informed and thoughtful choices that shape our future.

在决策领域，我们经常会遇到各种路径，这些路径将我们引向不同的方向。这些路径可以被视为bifurcations，一个单一的路线分为两个不同的选项。理解bifurcations不仅在我们的个人生活中至关重要，在数学、生物学甚至社会科学等领域也是如此。每一个bifurcation代表着一个选择，一个时刻，我们必须权衡我们的选项并考虑每条路径可能带来的后果。 例如，考虑一个简单的场景：你在职业生涯中处于十字路口。你有两个工作机会，每个机会都有其自身的优缺点。你决定追求其中一个而不是另一个的那一刻就是一个经典的bifurcation例子。这个决定可能会对你的未来产生重大影响，塑造你的职业轨迹和个人满足感。在这种情况下，认识到bifurcations的本质帮助我们欣赏选择的重大性。 在数学中，bifurcations指的是系统参数的小变化导致其行为发生突然的定性变化的点。例如，在动态系统中，一个bifurcation可能意味着从稳定平衡转变为混沌行为。这个概念对于建模复杂系统的科学家和工程师至关重要，因为它使他们能够预测初始条件的变化如何导致截然不同的结果。通过研究bifurcations，我们获得了关于系统稳定性和转变的洞察，帮助我们做出有关其未来状态的明智预测。 在生物学中，bifurcations可以在进化过程中观察到。当物种从共同祖先中分化时，它们经历了进化路径上的bifurcations，导致了我们今天所看到的生命多样性。理解这些进化bifurcations帮助生物学家追踪物种的谱系，并理解自然选择的机制。每一个进化中的bifurcation都说明了生物如何适应其环境，强调了这些决策在物种生存中的重要性。 此外，在社会科学中，bifurcations可以代表社会规范或行为发生显著变化的时刻。例如，在重大政治运动期间，社会可能会经历公众舆论的bifurcations，在不同信仰和价值观的基础上分裂成不同的群体。认识到这些bifurcations使社会学家能够分析社会趋势的变化，并理解推动集体行为的因素。 总之，bifurcations是发生在生活各个领域的重要时刻。它们象征着可能导致完全不同结果的选择，无论是在个人决策、数学模型、生物进化还是社会变迁中。通过理解bifurcations，我们更加意识到我们世界的复杂性以及我们所做决策的关键性质。接受bifurcations的概念使我们能够更有洞察力地应对生活中的挑战，最终导致更明智和深思熟虑的选择，从而塑造我们的未来。