Strong desynchronizing effects of weak noise in globally coupled systems

Area of Science:

• Dynamical systems theory
• Nonlinear dynamics
• Statistical physics

Background:

• Globally coupled dynamical units can synchronize, forming a cloud in phase space.
• Weak independent noise can perturb these units, leading to complex behaviors.
• Nonperiodic noise-free dynamics are crucial for observing specific phenomena.

Purpose of the Study:

• To investigate anomalous dispersion in synchronized dynamical systems under weak noise.
• To analyze the multiscaling properties of the synchronized cloud's linear dimension.
• To interpret the observed behavior using stochastic processes.

Main Methods:

• Numerical simulations of globally coupled dynamical units.
• Analysis of moments of the cloud's linear dimension as a function of noise strength.
• Modeling the phenomenon using a multiplicative stochastic process with small additive noise.

Main Results:

• Weak noise induces anomalous dispersion in the synchronized cloud.
• Multiscaling behavior is observed in the cloud's linear dimension with parameter-dependent exponents.
• The phenomenon can be explained by a multiplicative stochastic process.

Conclusions:

• Anomalous dispersion and multiscaling are key features in synchronized nonperiodic dynamical systems with weak noise.
• The findings provide a framework for understanding complex behaviors in such systems.
• The universality of this phenomenon is suggested, with implications for various scientific fields.