Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

Area of Science:

• Nonlinear dynamics
• Complex systems
• Network science

Background:

• Chimera states, characterized by localized frequency synchrony, are complex phenomena observed in coupled oscillator networks.
• Generating and controlling chimera states in realistic systems remains a significant challenge.

Purpose of the Study:

• To present a general and robust method for generating chimera dynamics in two-population oscillator networks.
• To bridge the gap between theoretical phase models and experimental realizations of chimera states.

Main Methods:

• A novel approach utilizing delayed interactions with both linear and quadratic coupling terms.
• Phase-model-based design to determine optimal delay and interaction component ratios.
• Demonstration using the Brusselator model and experimental electrochemical oscillators.

Main Results:

• Successfully generated robust chimera dynamics in two-population oscillator networks.
• Validated the effectiveness of the designed coupling strategy across different models and experimental setups.
• Established a direct link between phase model predictions and real-world oscillator network behavior.

Conclusions:

• The proposed method provides a versatile and effective means to induce and control chimera dynamics.
• This technique facilitates the study of chimera states in more complex and realistic oscillatory systems.
• Opens new avenues for exploring synchronization phenomena in coupled dynamical systems.