Influence of colored noise on chaotic systems

Area of Science:

• Nonlinear dynamics and chaos theory.
• Statistical physics and noise analysis.

Background:

• Classical chaotic systems are susceptible to noise, affecting dynamical properties.
• White noise is known to degrade scaling regions in chaotic attractors.
• Understanding noise effects is crucial for accurate analysis of chaotic systems.

Purpose of the Study:

• To investigate the impact of white and colored noise on correlation dimension and Kolmogorov entropy.
• To analyze the dependence of these measures on noise level and spectral exponent.
• To determine if colored noise preserves scaling properties in chaotic systems.

Main Methods:

• Numerical simulations of classical chaotic systems subjected to different noise types.
• Calculation of correlation dimension and Kolmogorov entropy.
• Analysis of the correlation sum and scaling region width.
• Varying noise levels and spectral exponents.

Main Results:

• White noise significantly reduces the scaling region width for correlation dimension and entropy.
• Colored noise minimally obscures the scaling region, altering correlation sum shape at small scales.
• A noise level of ~5% still yields a discernible plateau for the correlation sum.
• Calculated correlation dimension shows a bilinear dependence on noise level and noise dimension (linked to spectral exponent).
• Scaling region width for correlation entropy depends on the spectral exponent, while plateau values remain largely unchanged.

Conclusions:

• Colored noise is less disruptive to the scaling properties of chaotic systems compared to white noise.
• The spectral exponent of colored noise influences the scaling region width of correlation entropy.
• Correlation dimension is predictably affected by noise level and its spectral characteristics.