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Phase diagram of a generalized Winfree model
F Giannuzzi1, D Marinazzo, G Nardulli
1Dipartimento Interateneo di Fisica, Università di Bari, Bari, Italy. floriana.giannuzzi@ba.infn.it
Summary
This study modifies the Winfree model by coupling strength dependent on oscillator synchronization. Lowering the exponent z expands the synchronized phase, making incoherent behavior less typical in coupled systems.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- The Winfree model describes coupled oscillators, crucial in fields like neuroscience and physics.
- Real-world systems exhibit coupling that varies with synchronization levels, deviating from standard models.
Purpose of the Study:
- To investigate a generalized Winfree model where coupling strength depends on the Kuramoto order parameter (r).
- To analyze how the exponent 'z' influences the phase diagram and transition dynamics.
Main Methods:
- Analytical and numerical approaches were employed.
- The study focused on the parameter 'z' controlling coupling strength as a function of synchronization (r).
Main Results:
- The exponent 'z' dictates the size of the incoherent phase region.
- Choosing z<1 expands the synchronized (locked) phase, making incoherent behavior less common.
- Partial locked behavior vanishes for z>1.
Conclusions:
- The generalized Winfree model offers richer dynamics than the standard Winfree model.
- The nature of the phase transition (continuous vs. first-order) depends on the value of 'z'.
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