Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

89
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
89
Second Order systems II01:18

Second Order systems II

96
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.
96
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

81
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
81
Multimachine Stability01:25

Multimachine Stability

150
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
150
Second Order systems I01:20

Second Order systems I

144
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.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
144
Control System Problem01:21

Control System Problem

111
In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
111

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Optimized predefined-time control for high-order nonlinear MASs via ICA and reinforcement learning.

ISA transactions·2026
Same author

Data-Driven Optimized Output Regulation for Markov Jump Linear Systems and Its Application.

IEEE transactions on cybernetics·2026
Same author

Turing instability and pattern formation in a diffusive predator-prey system with opportunistic predators and weak Allee effect.

Physical review. E·2026
Same author

Containment control for stochastic multiagent systems with multiple dynamic leaders and compound noises.

ISA transactions·2026
Same author

Stochastic-Sampling-Based Event-Triggered Control for Switching Reaction-Diffusion Neural Networks.

IEEE transactions on cybernetics·2026
Same author

Passivity and synchronization of fractional-order coupled neural networks with multiple weights: A PD approach.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Hidden Data Recovery and Forecasting via Next-Generation Reservoir Computing With Multiscale Delay Selection.

IEEE transactions on neural networks and learning systems·2026
Same journal

CAFF-CIL: Causality-Aware Freedom Forgetting Approach for Class-Incremental Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Harmonic Autoencoding Framework for Multiple Tasks in Magnetic Particle Imaging Reconstruction.

IEEE transactions on neural networks and learning systems·2026
Same journal

A Survey on Human-Centric Voice-Face Multimodal Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Vision-Assisted Foundation Model for Solving Multitask Vehicle Routing Problems.

IEEE transactions on neural networks and learning systems·2026
Same journal

FP3O: Enabling Proximal Policy Optimization in Multiagent Cooperation With Parameter-Sharing Versatility.

IEEE transactions on neural networks and learning systems·2026
See all related articles

Related Experiment Video

Updated: Jun 23, 2025

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

10.3K

Stability and Dynamics Analysis of Time-Delay Fractional-Order Large-Scale Dual-Loop Neural Network Model With

Xiangyu Du, Min Xiao, Jianlong Qiu

    IEEE Transactions on Neural Networks and Learning Systems
    |June 19, 2024
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a large-scale fractional-order dual-loop neural network model. Time delays significantly influence Hopf bifurcation, impacting stability in complex neural network dynamics.

    More Related Videos

    Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
    08:08

    Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

    Published on: June 24, 2015

    11.5K
    Assessment of the Effects of Endocrine Disrupting Compounds on the Development of Vertebrate Neural Network Function Using Multi-electrode Arrays
    08:28

    Assessment of the Effects of Endocrine Disrupting Compounds on the Development of Vertebrate Neural Network Function Using Multi-electrode Arrays

    Published on: April 26, 2018

    6.0K

    Related Experiment Videos

    Last Updated: Jun 23, 2025

    Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
    11:18

    Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

    Published on: March 2, 2015

    10.3K
    Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
    08:08

    Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

    Published on: June 24, 2015

    11.5K
    Assessment of the Effects of Endocrine Disrupting Compounds on the Development of Vertebrate Neural Network Function Using Multi-electrode Arrays
    08:28

    Assessment of the Effects of Endocrine Disrupting Compounds on the Development of Vertebrate Neural Network Function Using Multi-electrode Arrays

    Published on: April 26, 2018

    6.0K

    Area of Science:

    • Computational Neuroscience
    • Dynamical Systems Theory
    • Fractional Calculus

    Background:

    • Existing research on annular neural networks often simplifies network structures.
    • Limited exploration of complex coupling modes and large-scale networks exists.
    • Fractional-order derivatives offer a more accurate description of neural dynamics.

    Purpose of the Study:

    • To establish a large-scale time-delay fractional-order dual-loop neural network model.
    • To analyze the stability and Hopf bifurcation of this complex network.
    • To investigate the influence of various parameters on network dynamics.

    Main Methods:

    • Developed a fractional-order dual-loop neural network model using Caputo fractional derivatives.
    • Employed the Coates flow graph method to derive the characteristic equation.
    • Utilized the holistic element method and magnitude angle formula for analysis.

    Main Results:

    • Derived stability and Hopf bifurcation criteria for the proposed network.
    • Identified key parameters influencing stability: fractional order, neuron count, distribution, and self-feedback coefficients.
    • Demonstrated that time delays significantly affect the amplitude and period of Hopf bifurcation.

    Conclusions:

    • The stability of the fractional-order dual-loop neural network is sensitive to multiple parameters.
    • Time delays play a crucial role in modulating the oscillatory behavior (Hopf bifurcation).
    • The developed model provides a more comprehensive framework for analyzing complex neural network dynamics.