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Spatiotemporal stability of one-way open coupled nonlinear systems
1Department of Electrical and Electronic Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531 Japan.
Summary
This study reveals that the H(infinity) norm predicts spatial instability in coupled nonlinear systems. Instability arises when the H(infinity) norm exceeds 1, confirmed by simulations.
Area of Science:
- Nonlinear Dynamics
- Control Theory
- Complex Systems
Background:
- Homogeneous solutions in coupled nonlinear systems can exhibit spatiotemporal instabilities.
- Robust control theory utilizes the H(infinity) norm as a key performance index.
Purpose of the Study:
- To investigate the spatiotemporal stability of homogeneous solutions in one-way open coupled nonlinear systems.
- To demonstrate the utility of the H(infinity) norm in understanding spatial instability mechanisms.
Main Methods:
- Application of the H(infinity) norm concept from robust control theory.
- Analysis of the transfer function of individual sites within coupled systems.
- Numerical simulations of one-way open coupled double scroll circuits.
Main Results:
- The H(infinity) norm effectively characterizes the spatial instability in coupled systems.
- Spatial instability is shown to occur if and only if the H(infinity) norm of each site's transfer function is greater than 1.
- Numerical simulations align well with the theoretical predictions.
Conclusions:
- The H(infinity) norm provides a critical threshold for predicting spatial instability in these systems.
- This framework offers a robust method for analyzing and potentially controlling instabilities in coupled nonlinear systems.
- The findings are validated by experimental results from double scroll circuits.
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