Controlling spatiotemporal chaos in coupled map lattices

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Chaos Theory

Background:

• Spatiotemporal chaos is prevalent in coupled map lattices (CML).
• Controlling chaotic behavior to achieve ordered states is a significant challenge.
• Existing methods may lack broad applicability or simplicity.

Purpose of the Study:

• To present a simple and effective method for controlling spatiotemporal chaos.
• To achieve a homogeneous state from chaotic dynamics in CML.
• To demonstrate the method's applicability to diverse CML models.

Main Methods:

• Development of a novel control strategy for CML.
• Stability analysis of the targeted homogeneous state.
• Application and validation across different CML configurations (e.g., open-flow, globally coupled).

Main Results:

• A simple and sufficient condition for controlling chaos to a homogeneous state was derived.
• The method proved effective for coupled map lattices, one-way open CML, and globally coupled maps.
• Theoretical predictions showed excellent agreement with numerical simulation results.

Conclusions:

• The presented method offers a straightforward way to control spatiotemporal chaos in various coupled map lattice systems.
• The derived conditions ensure the stability of the homogeneous state.
• This work provides a valuable tool for researchers studying complex system dynamics and control.