Effect of multiplicative noise on stationary stochastic process

Area of Science:

• Statistical physics
• Nonlinear dynamics
• Complex systems analysis

Background:

• Open systems are fundamental in understanding various natural and technical phenomena.
• Analyzing systems with multiplicative noise presents unique challenges in predicting their behavior.
• The interplay between deterministic forces and random fluctuations is crucial for system stability.

Purpose of the Study:

• To investigate the behavior of an open system under the influence of multiplicative noise.
• To analyze the stationary state resulting from the balance of damping and noise.
• To study the dependence of statistical moments on system parameters, particularly noise characteristics.

Main Methods:

• Utilizing the Langevin equation framework to model the open system.
• Simulating random pumping as noise with controlled periodicity.
• Analyzing statistical moments of the system's characteristic variable.

Main Results:

• A balance between deterministic damping and controlled periodic noise establishes the system's stationary state.
• A nontrivial decrease in the mean value of the main variable was observed as noise stochasticity increased.
• The study quantifies the impact of noise parameters on system dynamics.

Conclusions:

• The behavior of open systems with multiplicative noise can be counterintuitive, with increased noise leading to decreased mean values.
• The findings have potential applications across diverse scientific and technical fields.
• Understanding noise-induced effects is critical for controlling and predicting the behavior of complex systems.