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Nonuniversal results induced by diversity distribution in coupled excitable systems
Luis F Lafuerza1, Pere Colet, Raul Toral
1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos, CSIC-UIB, Campus UIB, E-07122 Palma de Mallorca, Spain.
Physical Review Letters
|September 28, 2010
Summary
Disorder induces collective firing in active rotators. However, this transition is absent for the commonly used Lorentzian distribution, highlighting its limitations in modeling generic coupled oscillator systems.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Active rotator systems are crucial models for understanding collective behavior in various physical and biological systems.
- The excitable regime in these systems allows for transitions between resting and active states, leading to complex dynamics.
- Disorder, or heterogeneity in system parameters, can significantly alter collective phenomena.
Purpose of the Study:
- To investigate the impact of disorder on the collective firing transition in globally coupled active rotators near the excitable regime.
- To determine the generic conditions under which this collective firing transition occurs.
- To critically evaluate the suitability of the Lorentzian distribution for describing generic properties of coupled oscillators.
Main Methods:
- Analysis of a system of globally coupled active rotators.
- Introduction of disorder through parameter diversity.
- Mathematical analysis of the transition to collective firing.
- Comparison of results for various diversity distributions, including the Lorentzian distribution.
Main Results:
- A transition to collective firing is generically induced by disorder in active rotator systems.
- This transition is observed for any diversity distribution with well-defined moments.
- Crucially, the collective firing transition is absent when using the Lorentzian distribution.
Conclusions:
- The presence of disorder is a key factor in inducing collective firing in active rotator systems.
- The findings underscore that the Lorentzian distribution may not accurately represent the generic behavior of coupled oscillators.
- Caution is advised when employing Lorentzian distributions to study universal properties of oscillator networks.
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