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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.
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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

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Published on: February 9, 2017

Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.

Chiara Mocenni¹, Angelo Facchini, Antonio Vicino

¹Dipartimento di Ingegneria dell'Informazione, Università di Siena, Centro per lo Studio dei Sistemi Complessi, via Roma 56, 53100 Siena, Italy. mocenni@dii.unisi.it

Proceedings of the National Academy of Sciences of the United States of America

|April 21, 2010

Summary

This study introduces a novel method using spatial recurrence properties to detect structural changes in complex spatio-temporal systems. The technique successfully identified spiral wave stability changes and Turing bifurcations in reaction-diffusion models.

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Area of Science:

Complex Systems Dynamics
Nonlinear Science
Pattern Formation

Background:

Spatio-temporal systems far from equilibrium can display irregular behaviors, including pattern formation and chaos.
Reconstructing and identifying complex dynamical regimes is challenging with limited observational data.

Purpose of the Study:

To develop and validate a method for detecting structural changes in spatially distributed systems.
To analyze complex dynamical regimes in reaction-diffusion systems using spatial recurrence properties.

Main Methods:

Utilized generalized recurrence plots and generalized recurrence quantification analysis.
Developed diagrams based on spatial recurrence properties to detect system changes.
Applied the method to the complex Ginzburg-Landau and Schnakenberg systems.

Main Results:

Successfully detected structural changes in complex spatio-temporal systems.
Identified changes in the stability of spiral wave solutions in the complex Ginzburg-Landau equation.
Analyzed Turing bifurcations in the Schnakenberg system.

Conclusions:

Spatial recurrence analysis provides an effective tool for identifying dynamical regime shifts in complex systems.
The proposed method enhances the understanding of pattern formation and stability in reaction-diffusion systems.