Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

Stability of Equilibrium Configuration

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...

Routh-Hurwitz Criterion I

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...

Stability of structures

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

Multimachine Stability

Multimachine Stability

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:

Pole and System Stability

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

You might also read

Related Articles

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

Sort by

Same author

A Model for Evolutionary Structural Plasticity and Synchronization of a Network of Neurons.

Computational and mathematical methods in medicine·2021

Same author

American Sign Language Alphabet Recognition Using a Neuromorphic Sensor and an Artificial Neural Network.

Sensors (Basel, Switzerland)·2017

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 24, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

A direct complex-domain stability criterion for synchronization of complex-valued dynamical networks.

G Solís-Perales¹, J Rivera-Domínguez², J Sánchez-Estrada¹

¹Departamento de Ciencias Computacionales, Universidad de Guadalajara, Guadalajara, Jalisco, Mexico.

Chaos (Woodbury, N.Y.)

|June 22, 2026

Summary

We developed a direct complex-domain criterion for analyzing complex network synchronization. This method preserves system dimensions and structure, unlike real-domain transformations.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Related Experiment Videos

Last Updated: Jun 24, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Complex Systems
Network Science
Nonlinear Dynamics

Background:

Traditional synchronization analysis doubles system dimensions by splitting complex states into real and imaginary parts.
This transformation obscures the inherent behavior and structure of complex-valued systems.

Purpose of the Study:

To introduce a direct criterion in the complex domain (Cn) for analyzing local exponential synchronization in complex networks.
To preserve the system's intrinsic geometric and algebraic structure, avoiding dimension inflation.

Main Methods:

Developed a direct criterion applicable to both holomorphic and non-holomorphic complex-valued systems.
The criterion balances node dissipation, non-holomorphic destabilization, and diffusive coupling stabilization.
Applied the criterion to networks of Hamiltonian holomorphic oscillators and non-holomorphic Lorenz chaotic systems.

Main Results:

Demonstrated a novel criterion for analyzing complex network synchronization directly in the complex domain.
Validated the criterion's effectiveness through two numerical examples, including chaotic systems.
Showcased the preservation of system dimension and complex dynamic features.

Conclusions:

The proposed direct complex-domain criterion offers an alternative to traditional methods for synchronization analysis.
This approach is crucial for accurately studying complex-valued systems where preserving complex dynamics is essential.
The criterion provides insights into the interplay of dissipation, non-holomorphicity, and coupling in network synchronization.