Control of collective network chaos.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Large globally-coupled heterogeneous networks of coupled oscillators can exhibit low-dimensional chaotic behavior in their macroscopic mean field.
• Reduced ordinary differential equations have been developed to accurately capture this collective mean field behavior.

Purpose of the Study:

• To demonstrate the successful application of chaos control algorithms, designed using reduced equations, to imperfect realizations of full oscillator networks.
• To systematically evaluate the effectiveness of chaos control as conditions for the accuracy of reduced equations are relaxed.

Main Methods:

• Development of chaos control algorithms based on reduced ordinary differential equations describing network mean field dynamics.
• Application of these algorithms to full network models with varying degrees of imperfection (network size, coupling, heterogeneity).
• Quantitative measurement of control quality under relaxed conditions.

Main Results:

• Chaos control algorithms designed from reduced equations are effective even when applied to imperfect network realizations.
• The method demonstrates robustness to smaller network sizes, modest deviations from global coupling, and mild inaccuracies in heterogeneity estimates.
• The effectiveness is network-dependent but surprisingly broad.

Conclusions:

• Chaos control based on reduced equations offers a viable strategy for managing collective chaotic behavior in complex oscillator networks.
• The technique is more broadly applicable than initially suggested by the strict conditions required for the accuracy of the reduced models.