Diffusion in a two-dimensional anisotropic web map by extrinsic noise applied to the intrinsically perturbed quantity

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Studying diffusion in complex systems is crucial for understanding various physical phenomena.
• Anisotropic web mappings present unique challenges for diffusion analysis.
• Previous work showed extrinsic noise on passive quantities leads to anisotropic diffusion.

Purpose of the Study:

• To investigate the diffusion scaling in a 2D anisotropic web mapping.
• To analyze the effect of applying extrinsic noise to an intrinsically active physical quantity.
• To compare this behavior with cases where extrinsic noise is applied to intrinsically passive quantities.

Main Methods:

• Theoretical analysis of diffusion in a two-dimensional anisotropic web mapping.
• Mathematical modeling of extrinsic noise applied to an intrinsically active quantity.
• Comparison of diffusion scaling under different noise application scenarios.

Main Results:

• When extrinsic noise is applied to the intrinsically active quantity, diffusion scaling is isotropic.
• Intrinsic web diffusion is found to be negligible in this scenario.
• This isotropic diffusion contrasts with the highly anisotropic scaling observed when noise is applied to a passive quantity.

Conclusions:

• The location of extrinsic noise application significantly impacts diffusion scaling in anisotropic systems.
• Isotropic diffusion can emerge even in anisotropic systems under specific noise conditions.
• This finding offers new insights into controlling diffusion in complex physical mappings.