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Related Concept Videos

Second Order systems II01:18

Second Order systems II

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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.
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Second Order systems I01:20

Second Order systems I

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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Multi-input and Multi-variable systems01:22

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Outer synchronization and outer H∞ synchronization for coupled fractional-order reaction-diffusion neural networks

Jin-Liang Wang1, Si-Yang Wang1, Yan-Ran Zhu1

  • 1Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, School of Computer Science and Technology, Tiangong University, Tianjin 300387, China.

Neural Networks : the Official Journal of the International Neural Network Society
|November 15, 2024
PubMed
Summary

This study explores outer synchronization and outer H∞ synchronization for coupled fractional-order reaction-diffusion neural networks (CFRNNs). New synchronization conditions were derived and validated using numerical examples.

Keywords:
Coupled fractional-order reaction–diffusion neural networks (CFRNNs)Multiple spatial-diffusion couplingsMultiple state couplingsOuter H(∞) synchronizationOuter synchronization

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Area of Science:

  • Control Theory
  • Computational Neuroscience
  • Fractional Calculus

Background:

  • Coupled fractional-order reaction-diffusion neural networks (CFRNNs) are complex systems with applications in various fields.
  • Understanding synchronization phenomena in these networks is crucial for their effective utilization.
  • Existing models may not fully capture the dynamics of spatial-diffusion coupled systems.

Purpose of the Study:

  • To introduce and analyze multiple state or spatial-diffusion coupled fractional-order reaction-diffusion neural networks (CFRNNs).
  • To investigate the outer synchronization and outer H∞ synchronization problems for these CFRNNs.
  • To develop novel conditions for achieving outer and outer H∞ synchronization.

Main Methods:

  • Lyapunov functional method
  • Laplace transform
  • Inequality techniques
  • Analysis of coupled fractional-order systems

Main Results:

  • Established conditions for achieving outer synchronization in CFRNNs.
  • Developed criteria ensuring outer H∞ synchronization for CFRNNs.
  • Demonstrated the validity of the derived conditions through two numerical examples.

Conclusions:

  • The proposed methods effectively address outer and outer H∞ synchronization in spatial-diffusion coupled CFRNNs.
  • The findings contribute to the theoretical understanding and practical application of fractional-order neural networks.
  • Numerical simulations confirm the robustness and accuracy of the derived synchronization conditions.