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Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling.
Chenggui Yao1, Meng Zhan2, Jianwei Shuai3
1Department of Mathematics, Shaoxing University, Shaoxing, China.
Chaos (Woodbury, N.Y.)
|January 1, 2018
Summary
Time delay significantly impacts the coupling strength needed for complete synchronization in chaotic pendulum networks. Network structure, however, does not affect this synchronization threshold.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Collective dynamical behaviors in complex systems are influenced by time delays and network structure.
- Synchronization is a key collective behavior observed in various complex systems.
Purpose of the Study:
- To investigate the influence of coupling strength, time delay, and network topology on synchronization in delay-coupled chaotic pendulum networks.
- To determine the relative importance of time delay versus network structure in achieving complete synchronization.
Main Methods:
- Numerical simulations of delay-coupled networks of chaotic pendulums.
- Analysis of synchronization thresholds under varying coupling strengths, time delays, and network topologies (regular, small-world, scale-free).
Main Results:
- The threshold coupling strength for complete synchronization is highly dependent on the time delay.
- Network topology (regular, small-world, scale-free) showed minimal impact on the synchronization threshold.
- Time delay induces a synchronous periodic state, which is crucial for achieving complete synchronization.
Conclusions:
- Time delay is a critical factor governing synchronization in these networks, more so than network structure.
- Understanding the role of time delay is essential for controlling and predicting collective dynamics in complex systems.
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