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Synchronous slowing down in coupled logistic maps via random network topology.
Sheng-Jun Wang1,2, Ru-Hai Du1,2, Tao Jin1,2
1Institute of Theoretical &Computational Physics, Shaanxi Normal University, Xi'an 710062, China.
Synchronization speed and paths are crucial for system function. This study reveals a novel slowing down phenomenon in coupled logistic maps, highlighting distinct synchronization pathways in low-dimensional dissipative systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Synchronization is vital for system function but its dynamics are understudied.
- Low-dimensional dissipative systems exhibit complex synchronization behaviors.
Purpose of the Study:
- Investigate the speed and paths of synchronization in coupled logistic maps.
- Identify novel phenomena and common features in synchronization processes.
Main Methods:
- Analysis of coupled multiple-period and multiple-band chaotic maps.
- Examination of system dynamics under varying coupling strengths (weak, strong, mediate).
- Utilizing finite-time Lyapunov exponent and its distribution to prove synchronization paths.
Main Results:
- Observed a novel slowing down phenomenon in the synchronization process.
- Identified two distinct transient synchronization paths.
- Demonstrated that weak coupling leads to local dynamics dominance, while strong coupling favors collective dynamics.
- Showcased the interplay between local and collective dynamics in mediate coupling, causing the slowing down.
Conclusions:
- Synchronization pathways significantly influence system dynamics.
- The slowing down of synchronization is a key phenomenon in coupled systems.
- Understanding these distinct paths is crucial for characterizing complex system behavior.
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