Noise induced bistability of parametric surface waves.

Area of Science:

• Nonlinear Dynamics
• Fluid Mechanics
• Wave Phenomena

Background:

• Subcritical bifurcations are critical points where a system can exist in multiple stable states.
• Surface waves are fundamental in various physical and engineering applications.
• External noise can significantly influence the behavior of nonlinear systems.

Purpose of the Study:

• To experimentally investigate the impact of external multiplicative noise on subcritical bifurcations.
• To analyze the parametric amplification of surface waves under noisy conditions.
• To understand noise-induced transitions and bistability in this system.

Main Methods:

• Experimental setup to generate and control surface waves.
• Introduction of controlled external multiplicative noise.
• Measurement and analysis of wave amplitude probability density functions.
• Construction of bifurcation diagrams under varying noise levels.

Main Results:

• The probability density function of wave amplitude exhibited two maxima under noise, deviating from deterministic states.
• New branches appeared in the bifurcation diagram due to noise-induced most probable values.
• A significantly larger difference in oscillation amplitude was observed.
• The bistable region of the system was substantially enlarged.

Conclusions:

• External multiplicative noise induces bistability in subcritical bifurcations of surface waves.
• Noise-induced transitions provide a framework for understanding these new dynamic behaviors.
• The findings expand the understanding of noise effects in nonlinear wave systems.