The impact of inner-coupling and time delay on synchronization: From single-layer network to hypernetwork
Heng Guo1, Jin Zhou1, Shuaibing Zhu2
1School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
Chaos (Woodbury, N.Y.)
|December 1, 2022
Summary
This study explores how network parameters affect synchronization in hypernetworks using Rössler oscillators. Time delays significantly alter the synchronized region (SR) in unbounded hypernetworks, impacting both size and type.
Area of Science:
- Complex dynamical systems
- Network science
- Chaos theory
Background:
- Synchronization in complex dynamical systems is well-researched.
- Limited studies investigate network parameter impacts on hypernetwork synchronization.
- Hypernetworks present unique challenges for synchronization analysis.
Purpose of the Study:
- To investigate the influence of inner-coupling and time delay on the synchronized region (SR) in a coupled Rössler oscillator hypernetwork model.
- To analyze how different inner-coupling matrix forms affect the SR.
- To determine the role of time delays in various SR types.
Main Methods:
- Utilized a hypernetwork model composed of coupled Rössler oscillators.
- Employed three distinct inner-coupling matrix forms (bounded, unbounded, empty SR).
- Analyzed the effects of varying inner-couplings and time delays on the hypernetwork's SR.
Main Results:
- Inner-couplings and time delays significantly impact the SR, especially in unbounded cases.
- Unbounded SR in subnetworks leads to unbounded SR in the entire hypernetwork.
- Time delays can alter both the size and type of SR in unbounded hypernetworks.
- Time delays have minimal effect on the SR type in bounded or empty SR hypernetworks.
Conclusions:
- The structure of inner-coupling and the presence of time delays are critical factors in determining synchronization behavior in hypernetworks.
- Hypernetwork architecture can lead to complex synchronization phenomena, particularly with unbounded subnetworks.
- Understanding these parameters is crucial for designing and controlling synchronized complex systems.
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