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Reduction of the synchronization time in random logistic maps.

Kaito Sano¹, Takahito Mitsui^2,3, Takuma Akimoto⁴

¹Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Kashiwa 277-8561, Japan.

Physical Review. E

|January 20, 2021

Summary

Additive noise impacts nonchaotic logistic maps, altering Lyapunov exponents and orbit synchronization. Synchronization time is reduced by initial nonstationary behaviors, especially near the critical point.

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Area of Science:

Nonlinear dynamics
Chaos theory
Complex systems

Background:

The logistic map is a fundamental model in chaos theory.
Understanding the impact of noise on dynamical systems is crucial.
Synchronization phenomena in chaotic and nonchaotic systems are of significant interest.

Purpose of the Study:

To investigate the effects of additive noise on a nonchaotic logistic map.
To analyze the relationship between noise intensity, Lyapunov exponent, and orbit synchronization.
To identify factors influencing synchronization time in the presence of noise.

Main Methods:

Numerical simulations of the logistic map with additive noise.
Calculation of Lyapunov exponents for varying noise intensities.
Analysis of orbit synchronization and synchronization time.

Main Results:

The Lyapunov exponent transitions from negative to positive with increasing noise intensity.
Synchronization of orbits with different initial conditions occurs when the Lyapunov exponent is negative.
Synchronization time is not solely dependent on the Lyapunov exponent beyond a specific noise intensity.
A reduction in synchronization time is observed due to initial nonstationary behaviors.

Conclusions:

Additive noise significantly influences the dynamics of the nonchaotic logistic map.
Initial nonstationary behaviors, influenced by the critical point, play a key role in reducing synchronization time.
The interplay between noise, Lyapunov exponent, and nonstationary dynamics governs synchronization in this system.