在Kuramoto振荡器中具有更高阶相互作用的有限大小效应
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Chaos (Woodbury, N.Y.)
|October 11, 2024
概括
库拉莫托振荡器系统中具有更高阶相互作用的有限大小效应会比预测的更早地导致同步过渡. 这些效应还导致了新的部分同步状态,这种状态在较大的系统中是不可见的.
科学领域:
- 复杂的系统复杂的系统.
- 非线性动力学是一种非线性动力学.
- 统计物理学的统计物理.
背景情况:
- 有限大小的系统表现出独特的动态,特别是与共存的连贯和不连贯状态的多稳定性.
- 库拉莫托模型是研究合振荡器中的同步现象的标准框架.
研究的目的:
- 在全球合的库拉莫托振荡器中研究有限大小对高阶相互作用的同步过渡的影响.
- 探索有限尺寸的双种群振荡器系统中新动态状态的出现.
主要方法:
- 库拉莫托模型的数值模拟与更高阶相互作用.
- 对订单参数大小的第一个退出时间分布的分析.
- 计算不同系统大小的数值转换概率.
- 检查两个人群系统中的顺序参数的速度场.
主要成果:
- 与热力学极限相比,有限大小的波动推动了较早的同步过渡.
- 一个新的固定点,代表一个部分同步状态,在有限大小的两个人口系统中出现.
- 这种部分同步状态不在热力学极限中.
结论:
- 有限大小的效应显著改变了同步动态,并可能导致新的新兴状态.
- 了解这些效应对于准确建模现实世界中的复杂系统具有有限的组件至关重要.
更多相关视频
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
8.4K
10:52Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
12.8K
相关概念视频
01:07Damped Oscillations
5.7K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
5.7K
01:06Forced Oscillations
6.5K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.5K
01:04Oscillations about an Equilibrium Position
5.3K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
5.3K
01:19Concept of Resonance and its Characteristics
5.0K
If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not...
5.0K
01:18Second Order systems II
92
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
92
01:20Types of Damping
6.4K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
6.4K