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Related Concept Videos

State Space Representation01:27

State Space Representation

472
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...
472
Multimachine Stability01:25

Multimachine Stability

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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:
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Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

285
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,...
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Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

440
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...
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Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

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A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Analytical treatment for cyclic three-state dynamics on static networks.

Chao-Ran Cai1,2, Zhi-Xi Wu3

  • 1School of Physics, Northwest University, Xi'an 710069, China.

Physical Review. E
|February 20, 2020
PubMed
Summary

This study addresses the dynamical correlation problem in physics, developing analytical solutions for cyclic three-state dynamics on static networks. Results show distinct behaviors for symmetric versus asymmetric models when compared to annealed networks.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Network Science

Background:

  • Dynamical processes on networks face the 'dynamical correlation problem' where mean-field methods fail.
  • Understanding local interactions is crucial, as unconnected nodes do not influence dynamics.
  • Analytical solutions for these problems are vital for theoretical advancements.

Purpose of the Study:

  • To derive explicit analytical solutions for cyclic three-state dynamics on static networks.
  • To investigate the impact of network structure (static vs. annealed) on dynamical processes.
  • To compare theoretical predictions with simulation results.

Main Methods:

  • Developed explicit analytical expressions for propagating size and threshold curves.
  • Studied four distinct cyclic three-state dynamics: Lotka-Volterra, directed migration, SIRS epidemic, and predator-prey with empty sites.
  • Compared dynamics on static networks with those on annealed networks.

Main Results:

  • Analytical solutions were derived for propagating size and threshold curves for all four models.
  • Symmetric models (Lotka-Volterra, directed migration) exhibit identical macroscopic behaviors on static and annealed networks.
  • Asymmetric models (SIRS, predator-prey) show more complex and different outcomes on static networks compared to annealed networks.
  • Theoretical predictions closely matched Monte Carlo simulation results.

Conclusions:

  • The study provides a robust theoretical framework for analyzing cyclic three-state dynamics on static networks.
  • Network topology significantly influences dynamics, especially for asymmetric models.
  • The developed analytical methods are validated by simulation, offering a reliable tool for future research.