Dipartimento di Fisica, Università di Napoli 'Federico II', Complesso Universitario Monte S Angelo Via Cintia, Napoli I-80126, Italy.
Nat Commun. 2013;4:2733. doi: 10.1038/ncomms3733.
Intrinsically noisy mechanisms drive most physical, biological and economic phenomena. Frequently, the system's state influences the driving noise intensity (multiplicative feedback). These phenomena are often modelled using stochastic differential equations, which can be interpreted according to various conventions (for example, Itô calculus and Stratonovich calculus), leading to qualitatively different solutions. Thus, a stochastic differential equation-convention pair must be determined from the available experimental data before being able to predict the system's behaviour under new conditions. Here we experimentally demonstrate that the convention for a given system may vary with the operational conditions: we show that a noisy electric circuit shifts from obeying Stratonovich calculus to obeying Itô calculus. We track such a transition to the underlying dynamics of the system and, in particular, to the ratio between the driving noise correlation time and the feedback delay time. We discuss possible implications of our conclusions, supported by numerics, for biology and economics.
内在噪声机制驱动着大多数物理、生物和经济现象。通常，系统的状态会影响驱动噪声的强度（乘法反馈）。这些现象通常使用随机微分方程来建模，根据不同的约定（例如 Ito 微积分和 Stratonovich 微积分）可以对其进行解释，从而导致定性不同的解决方案。因此，在能够根据新条件预测系统的行为之前，必须根据可用的实验数据确定随机微分方程-约定对。在这里，我们通过实验证明，给定系统的约定可能会随操作条件而变化：我们表明，噪声电路从服从 Stratonovich 微积分转变为服从 Ito 微积分。我们跟踪这种转变到系统的基础动力学，特别是到驱动噪声相关时间与反馈延迟时间的比值。我们讨论了我们的结论的可能影响，这些结论得到了数值的支持，适用于生物学和经济学。
