Noise-aided control of chaotic dynamics in a logistic map

Area of Science:

• Nonlinear dynamics
• Chaos theory
• Complex systems

Background:

• Controlling chaos involves stabilizing unstable periodic orbits within a chaotic system using small perturbations.
• Linear delayed-feedback strategies are common for achieving chaos control.
• The role of external noise in enhancing chaos control efficiency is an area of interest.

Purpose of the Study:

• To investigate the constructive role of external noise in improving the efficiency of chaos control.
• To analyze the effect of noise on a system under subthreshold control conditions.
• To explore the resonance effect in chaotic systems with superimposed noise.

Main Methods:

• Utilizing a logistic map as a model system for chaotic dynamics.
• Implementing a linear delayed-feedback control strategy.
• Introducing external noise to the system and observing its impact on control efficiency.

Main Results:

• A resonance effect was observed in system dynamics when noise was superimposed under subthreshold control.
• The presence of an optimal noise level was found to significantly decrease the time required to reach the target state.
• External noise can constructively aid in stabilizing chaotic systems.

Conclusions:

• External noise can play a beneficial role in controlling chaos, particularly under specific conditions.
• The findings highlight the potential for noise-assisted control in nonlinear systems.
• Further research into noise-induced phenomena in chaos control is warranted.