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Nonuniversal dependence of spatiotemporal regularity on randomness in coupling connections
Zahera Jabeen1, Sudeshna Sinha
1Institute of Mathematical Sciences, Chennai, India.
Summary
The impact of random connections on coupled oscillator networks depends heavily on local dynamics. Network order changes unpredictably with randomness, influenced by oscillator frequency.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Coupled nonlinear oscillators are fundamental to understanding emergent behavior in various systems.
- The influence of network topology, including randomness, on system dynamics is a key research area.
Purpose of the Study:
- To investigate how varying degrees of randomness in coupling connections affect the spatiotemporal dynamics of coupled nonlinear oscillators.
- To explore the relationship between local dynamics and the global network behavior.
Main Methods:
- Modeling a network of coupled nonlinear oscillators using sine-circle maps.
- Systematically varying the fraction of random coupling links (p).
- Analyzing the basin of attraction for spatiotemporal fixed points.
Main Results:
- The change in the basin of attraction is critically dependent on the nature of local oscillator dynamics.
- The effect of random links on spatiotemporal regularity is nonuniversal.
- The dependence of regularity on randomness varies significantly with the angular frequency of the oscillators, showing monotonic or nonmonotonic behavior.
Conclusions:
- The influence of random coupling on spatiotemporal order in oscillator networks is highly nonuniversal.
- Nodal dynamics play a crucial role in determining the system's response to varying connection randomness.
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