Synchronization of two coupled massive oscillators in the time-delayed Kuramoto model.
Esmaeil Mahdavi1, Mina Zarei1, Farhad Shahbazi2
1Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran.
Chaos (Woodbury, N.Y.)
|January 9, 2025
Summary
Time delay in coupled massive oscillators can lead to multiple stable states and complex behaviors like chaos. Increased inertia amplifies instability in phase-locked solutions.
Area of Science:
- Physics
- Network Science
- Dynamical Systems
Background:
- Real-world networks face operational constraints due to signal transmission speed limitations.
- The second-order Kuramoto model is a fundamental framework for studying coupled oscillator systems.
Purpose of the Study:
- To investigate the influence of time delay on the dynamics of two coupled massive oscillators.
- To analyze the emergence of multi-stability and complex behaviors in the presence of inertia and time delay.
Main Methods:
- Analytical exploration of the second-order Kuramoto model.
- Numerical simulations to observe system dynamics.
- Characterization of phase-locked and non-phase-locked solutions.
Main Results:
- Time delay induces multi-stability in phase-locked solutions.
- Increased inertia reduces the stability of phase-locked states.
- Non-phase-locked solutions exhibit periodic and chaotic dynamics, dependent on inertia and time delay.
Conclusions:
- Time delay is a critical factor influencing the stability and behavior of coupled oscillator networks.
- The interplay between inertia and time delay dictates the transition to complex dynamics, including chaos.
- Findings are relevant for understanding and designing robust real-world networks with signal transmission constraints.
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