Transient chimera states emerging from dynamical trapping in chaotic saddles

Area of Science:

• Nonlinear Dynamics
• Network Science
• Chaos Theory

Background:

• Nonlinear systems with chaotic saddles can exhibit transient chaotic dynamics before settling into stable states.
• Coupled nonlinear systems are known to display complex emergent behaviors.

Purpose of the Study:

• To investigate the formation and characteristics of chimera states in networked nonlinear systems with nonlocal coupling.
• To analyze the transient dynamics and stability of these chimera states.

Main Methods:

• Modeling nonlinear systems with chaotic saddles in a ring network with nonlocal coupling.
• Implementing transversal stability analysis to assess the stability of synchronized states.
• Analyzing the lifetime and termination dynamics of observed chimera states.

Main Results:

• Demonstrated the emergence of two distinct transient chimera states (abrupt and gradual termination).
• Identified an optimal coupling range that maximizes the lifetime of these chimera states.
• Confirmed the asymptotic stability of the synchronized (coherent) domain within the chimera states.

Conclusions:

• Transient chimera states can be formed in networked nonlinear systems with chaotic saddles.
• The lifetime and stability of these states are dependent on network parameters like coupling range and size.
• These findings contribute to understanding complex dynamics in coupled chaotic systems.