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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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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...
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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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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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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.
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Related Experiment Video

Updated: Mar 7, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo
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Design and implementation of a heterogeneous multi-cavity hyperchaotic map derived from complex exponential

Zeping Zhang1, Huihai Wang1, Kehui Sun2

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

Chaos (Woodbury, N.Y.)
|March 5, 2026
PubMed
Summary
This summary is machine-generated.

A novel complex exponential chaotic map (CECM) and heterogeneous multi-cavity hyperchaotic map (HMCM) were developed to increase structural complexity. Dynamical analyses and hardware implementation confirm robust hyperchaotic performance and low resource usage.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Science
  • Chaos Theory

Background:

  • Enhancing structural complexity in multi-cavity chaotic maps is crucial for advanced applications.
  • Existing chaotic maps often lack sufficient complexity for sophisticated systems.

Purpose of the Study:

  • To introduce a new complex exponential chaotic map (CECM) for increased structural complexity.
  • To develop a heterogeneous multi-cavity hyperchaotic map (HMCM) by integrating CECM with step functions.
  • To verify the hyperchaotic performance and hardware feasibility of the proposed map.

Main Methods:

  • Development of a novel complex exponential chaotic map (CECM).
  • Integration of CECM with step functions to create a heterogeneous multi-cavity hyperchaotic map (HMCM).
  • Dynamical analyses including phase diagrams, Lyapunov exponents, and permutation entropy.
  • Implementation on a digital signal processor (DSP) for on-chip analysis.

Main Results:

  • The CECM exhibits parameter-sensitive attractor shapes.
  • The HMCM generates multiple cavities with unique structures, significantly enhancing system complexity.
  • Dynamical analyses confirm robust hyperchaotic behavior across a wide parameter range.
  • Hardware implementation on DSP validates physical feasibility, stable chaos, and low resource requirements.

Conclusions:

  • The proposed HMCM offers enhanced structural complexity and robust hyperchaotic performance.
  • The map is suitable for hardware implementation due to its low-resource usage and physical feasibility.
  • This work contributes a novel approach to designing complex chaotic systems for potential applications.