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Stochastic webs and their applications.

George M. Zaslavsky¹

¹Space Research Institute, ul. Profsoyuznaya 84/32, Moscow 117810Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012.

Chaos (Woodbury, N.Y.)

|July 1, 1991

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Researchers analyzed stochastic webs in dynamic systems and physical problems. They examined web properties, diffusion dynamics, and stochastic percolation phenomena.

Area of Science:

Physics
Dynamical Systems

Background:

Stochastic webs arise in degenerate dynamic systems.
Understanding their formation and properties is crucial in various physical problems.

Purpose of the Study:

Analyze conditions for stochastic web appearance in dynamic systems.
Investigate web symmetry, width, and structural changes.
Examine diffusion dynamics and stochastic percolation.

Main Methods:

Analysis of degenerate dynamic systems.
Examination of typical physical problems leading to stochastic webs.
Study of web properties and diffusion dynamics.

Main Results:

Conditions for stochastic web formation identified.

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Symmetry, width, and structural changes of webs described.

Diffusion dynamics variation with degrees of freedom and stochastic percolation discussed.

Conclusions:

Stochastic webs are a significant feature in certain dynamic systems.
Web properties and diffusion dynamics are dependent on system parameters.
Stochastic percolation is a key phenomenon associated with these webs.