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Delayed stochastic systems

Ohira¹, Yamane

¹Sony Computer Science Laboratory, 3-14-13 Higashi-gotanda, Shinagawa, Tokyo 141, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|October 25, 2000

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This study explores complex behaviors in delayed stochastic systems, combining noise and time delays. Researchers developed models and derived an approximate Fokker-Planck equation to understand these intricate natural systems.

Area of Science:

Physics
Mathematics
Complex Systems

Background:

Natural systems often exhibit complex behaviors due to inherent noise and time delays.
The interplay between noise and time delay in stochastic systems remains underexplored.
Understanding these combined effects is crucial for modeling diverse natural phenomena.

Purpose of the Study:

To investigate the complexity of delayed stochastic systems by considering both dynamical and probabilistic perspectives.
To gain insight into systems characterized by both noise and time delays.
To establish a theoretical framework for analyzing such systems.

Main Methods:

Focus on a Langevin equation with time delay.
Utilize a delayed random walk model where transition probabilities depend on past states.

Related Experiment Videos

Derive an approximate Fokker-Planck equation for delayed stochastic systems.

Main Results:

Establish connections between the Langevin and delayed random walk models.
Obtain an approximate Fokker-Planck equation applicable to delayed stochastic systems.
Compare the derived equation's solutions with numerical simulation results.

Conclusions:

The study provides a foundational understanding of delayed stochastic systems.
The derived Fokker-Planck equation offers a valuable tool for analyzing systems with noise and delay.
Further research can build upon these findings to model more complex natural phenomena.