Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization

Area of Science:

• Complex Networks
• Nonlinear Dynamics
• Excitable Media

Background:

• Self-sustained oscillations are crucial in excitable complex networks.
• Predicting and realizing these oscillations in diverse networks remains challenging.
• Winfree loop sustained oscillations (WLSO) are a key focus in 2D excitable lattices.

Purpose of the Study:

• To investigate the prediction and realization of WLSO in 2D excitable lattices.
• To identify and analyze the fundamental oscillation source structure (FOSS) responsible for WLSO.
• To develop a method to overcome limitations hindering spontaneous WLSO in 2D lattices.

Main Methods:

• Analysis of network structure to expose the FOSS.
• Calculation of minimum Winfree loop length for parameter prediction.
• Numerical simulations to confirm predictions and validate the targeted protection scheme.

Main Results:

• The FOSS of WLSO in 2D excitable lattices was explicitly identified.
• Suitable parameter combinations for self-organization of Winfree loops on FOSS were predicted and confirmed.
• A targeted protection scheme successfully overcame coupling bidirectionality and symmetry issues.

Conclusions:

• WLSO can be predicted and realized in 2D excitable lattices by understanding and manipulating the FOSS.
• The proposed protection scheme is effective in enabling sustained oscillations.
• This work provides a pathway for controlling oscillations in complex excitable systems.