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相关概念视频

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

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An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
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Hyperbolic Functions01:25

Hyperbolic Functions

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A flexible cable suspended between two points at the same height naturally forms a curve known as a catenary. This shape results from the balance between the cable’s weight and the tension acting along its length, representing a state of mechanical equilibrium. Unlike simpler approximations, the true shape of a hanging cable is described using hyperbolic functions.Hyperbolic functions are closely related to exponential functions and are named for their connection to the geometry of the...
103
Inverse Hyperbolic Functions and Their Derivatives01:25

Inverse Hyperbolic Functions and Their Derivatives

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The shape of a suspension bridge cable hanging under its own weight is described by a catenary curve, which is modeled using the hyperbolic cosine function. This mathematical model accurately captures the balance between gravity and tension acting along the cable. When a particular vertical position on the cable is known, the corresponding horizontal position can be determined using the inverse hyperbolic cosine function, allowing for a detailed analysis of the cable's geometry.Inverse...
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Design Example: Capacitance Multiplier Circuit01:20

Design Example: Capacitance Multiplier Circuit

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In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
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Hyperbolas01:30

Hyperbolas

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A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
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State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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从复杂的指数函数推导出异质的多空洞超混沌地图的设计和实现.

Zeping Zhang1, Huihai Wang1, Kehui Sun2

  • 1School of Electronic Information, Central South University, Changsha 410083, China.

Chaos (Woodbury, N.Y.)
|March 5, 2026
PubMed
概括

开发了一种新的复杂指数混沌地图 (CECM) 和异质的多腔超混沌地图 (HMCM),以增加结构复杂性. 动态分析和硬件实现证实了强大的超混沌性能和低资源使用.

科学领域:

  • 复杂系统动力学 复杂系统动力学
  • 非线性科学 非线性科学
  • 混沌理论 混沌理论

背景情况:

  • 在多腔混沌地图中增强结构复杂性对于高级应用至关重要.
  • 现有的混乱地图往往缺乏足够复杂的复杂性,用于复杂的系统.

研究的目的:

  • 为了增加结构复杂性,引入一个新的复杂指数混沌地图 (CECM).
  • 通过将CECM与步骤函数集成,开发一个异质的多腔超混沌地图 (HMCM).
  • 为了验证拟议地图的超混沌性能和硬件可行性.

主要方法:

  • 开发一个新的复杂指数混沌地图 (CECM).
  • 将CECM与步骤函数集成,以创建一个异质的多腔超混沌地图 (HMCM).
  • 动态分析,包括相位图,利亚普诺夫指数和变量.
  • 在数字信号处理器 (DSP) 上实现芯片内分析.

主要成果:

  • CECM展示了参数敏感的吸引器形状.
  • HMCM产生了具有独特结构的多个空洞,显著提高了系统的复杂性.
  • 动态分析证实了在一个广泛的参数范围内强大的超混沌行为.

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  • 在DSP上硬件实现验证了物理可行性,稳定的混乱和低资源需求.

    • 结论:

    • 拟议的HMCM提供了增强的结构复杂性和强大的超混沌性能.
    • 该地图适合硬件实现,因为其资源使用量低,并且具有物理可行性.
    • 这项工作为设计潜在应用的复杂混乱系统提供了一种新的方法.