Chimera states in coupled logistic maps with additional weak nonlocal topology

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Chimera states represent a fascinating phenomenon in complex systems, characterized by coexisting domains of synchronized and desynchronized behavior.
• Understanding the conditions for the emergence and stability of chimera states is crucial for various fields, including neuroscience and engineering.

Purpose of the Study:

• To investigate the occurrence and robustness of chimera states in globally coupled logistic map networks.
• To explore the impact of weak nonlocal topology and network modifications on chimera state stability.

Main Methods:

• Utilizing globally coupled logistic maps to model network dynamics.
• Introducing weak nonlocal topology and systematically altering network connections (disconnecting nodes, introducing symmetric gaps).
• Employing recurrence quantification analysis and computing the strength of incoherence to validate results.

Main Results:

• Demonstrated the existence of chimera states in networks of logistic maps with weak nonlocal topology.
• Showed that chimera states persist even after disconnecting nonlocal connections of some nodes.
• Confirmed the existence of chimera states with symmetric gaps in nonlocal coupling.
• Observed chimeralike states in small-world networks influenced by weak nonlocal topology.

Conclusions:

• Chimera states exhibit significant robustness to network modifications, including partial disconnection and introduction of gaps in nonlocal coupling.
• Weak nonlocal topology plays a critical role in inducing and sustaining chimera states in coupled map networks.
• The findings extend the understanding of chimera state dynamics to small-world network architectures.