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

Multi-input and Multi-variable systems

Multi-input and Multi-variable systems

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.
In the absence of...

Sequence Networks of Rotating Machines

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...

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:

State Space Representation

State Space Representation

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...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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, the...

You might also read

Related Articles

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

Sort by

Same author

Algebraic Statistics of Poincaré Recurrences in a DNA Molecule.

Physical review letters·2015

Same author

Symmetry breaking for ratchet transport in the presence of interactions and a magnetic field.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013

Same author

Poincaré recurrences of DNA sequences.

Physical review. E, Statistical, nonlinear, and soft matter physics·2012

Same author

Quantum vacuum of strongly nonlinear lattices.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011

Same author

Poincaré recurrences in Hamiltonian systems with a few degrees of freedom.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011

Same author

Google matrix and Ulam networks of intermittency maps.

Physical review. E, Statistical, nonlinear, and soft matter physics·2010

Search research articles

Related Experiment Video

Updated: Jun 14, 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

Google matrix, dynamical attractors, and Ulam networks.

D L Shepelyansky¹, O V Zhirov

¹Laboratoire de Physique Théorique (IRSAMC), Université de Toulouse-UPS, F-31062 Toulouse, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study models the Google matrix using dynamical systems, revealing networks with web-like properties. Changes in parameters can disrupt PageRank, leading to inefficient search results.

Related Experiment Videos

Last Updated: Jun 14, 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

Area of Science:

Complex Systems
Network Science
Dynamical Systems

Background:

The Google matrix, derived from the Perron-Frobenius operator, models complex networks.
Dynamical systems with dissipation can exhibit properties analogous to real-world networks like the World Wide Web.

Purpose of the Study:

To investigate the properties of a Google matrix generated from a coarse-grained Perron-Frobenius operator of a dissipative dynamical system.
To explore the network characteristics and PageRank behavior of the resulting Ulam networks.

Main Methods:

Construction of a finite-size matrix approximant using the Ulam method.
Analysis of the generated directed Ulam networks for scale-free properties and PageRank distribution.
Comparison of network characteristics with the World Wide Web.

Main Results:

The Ulam networks exhibit approximate scale-free scaling and degree distributions.
PageRank demonstrates a power-law decay, similar to the World Wide Web, with sensitivity to the Google parameter alpha.
Dynamical attractors concentrate PageRank, acting like popular websites.

Conclusions:

Dynamical systems can generate networks with web-like characteristics.
Parameter variations in the dynamical map can lead to PageRank delocalization and inefficient search behavior.