Complete synchronization of the global coupled dynamical network induced by Poisson noises

Area of Science:

• Dynamical systems
• Network theory
• Stochastic processes

Background:

• Investigating synchronization in complex networks is crucial for understanding emergent behaviors.
• The influence of noise, particularly Poisson noise, on network dynamics is not fully understood.
• Complete synchronization in globally coupled systems presents unique theoretical challenges.

Purpose of the Study:

• To investigate Poisson noise-induced complete synchronization in globally coupled dynamical networks.
• To establish theoretical conditions for achieving complete synchronization.
• To validate theoretical findings with numerical simulations.

Main Methods:

• Utilizing the stability theory of stochastic differential equations driven by a Poisson process.
• Developing mathematical conditions for guaranteed synchronization.
• Performing numerical simulations to verify theoretical predictions.

Main Results:

• Demonstrated that Poisson noise can indeed induce complete synchronization in the studied networks.
• Derived sufficient conditions that ensure complete synchronization with probability 1.
• Numerical results showed excellent agreement with the theoretical analysis.

Conclusions:

• Poisson noise is a viable mechanism for inducing complete synchronization in globally coupled dynamical networks.
• The established theoretical framework provides a robust method for predicting and achieving synchronization.
• The findings contribute to the understanding of noise effects in complex systems.