Spatiotemporal stability of one-way open coupled nonlinear systems

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.