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Impact of a leader on cluster synchronization
Sarika Jalan1,2, Aradhana Singh1, Suman Acharyya3
1Complex Systems Lab, Indian Institute of Technology Indore, Indore-452017, India.
A leader node with significant parameter mismatch changes cluster synchronization in coupled nonidentical oscillators. This leader induces a transition from driven to mixed cluster states, driven by frequency mismatch.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Coupled nonidentical oscillators are fundamental to understanding complex systems.
- Cluster synchronization is a key phenomenon in oscillatory networks.
- The role of specific nodes, like leaders, in network dynamics is crucial.
Purpose of the Study:
- To investigate the mechanisms of frequency-synchronized cluster formation.
- To analyze the impact of a 'leader' node on cluster synchronization.
- To understand how parameter mismatch influences cluster dynamics.
Main Methods:
- Simulation of coupled nonidentical oscillators.
- Analysis of cluster formation mechanisms.
- Characterization of synchronization states (driven, mixed).
Main Results:
- Introduction of a leader node significantly alters cluster patterns and formation mechanisms.
- A transition from driven to mixed cluster states is observed due to the leader's presence.
- Frequency mismatch is identified as the key factor driving this state transition.
Conclusions:
- Leaders profoundly impact cluster synchronization in nonidentical oscillator networks.
- The mechanism of cluster formation shifts based on the system's evolution (chaotic vs. periodic).
- Frequency mismatch plays a critical role in leader-induced transitions.
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