Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

Area of Science:

• Physics
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Many natural phenomena involve inherent noise.
• System behavior can depend on how noise is modeled.
• Stochastic differential equations have multiple interpretations (Itô and Stratonovich calculus).

Purpose of the Study:

• To experimentally investigate how the choice of calculus convention affects modeling of noisy systems.
• To determine if the calculus convention can change under different operational conditions.

Main Methods:

• Experimental setup using a noisy electric circuit.
• Tracking the circuit's dynamics under varying conditions.
• Analyzing the system's transition between Itô and Stratonovich calculus adherence.

Main Results:

• Demonstrated that a noisy electric circuit can shift between obeying Itô and Stratonovich calculus.
• Identified the ratio of driving noise correlation time to feedback delay time as a key factor in this transition.
• Observed a transition in calculus convention with changing operational conditions.

Conclusions:

• The appropriate calculus convention for modeling noisy systems is not fixed and can depend on operational conditions.
• The findings have potential implications for modeling in fields like biology and economics.
• Understanding this dynamic convention is crucial for accurate prediction of system behavior.