Observation of Saddle-Point Avoidance in Noise-Induced Escape
نویسندگان
چکیده
D. G. Luchinsky,1,2 R. S. Maier,3,4 R. Mannella,5 P. V. E. McClintock,1 and D. L. Stein4,3 1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom 2Russian Research Institute for Metrological Service, Ozernaya 46, 119361 Moscow, Russia 3Department of Mathematics, University of Arizona, Tucson, Arizona 85721 4Department of Physics, University of Arizona, Tucson, Arizona 85721 5Dipartimento di Fisica, Università di Pisa and INFM UdR Pisa, Piazza Torricelli 2, 56100 Pisa, Italy (Received 6 October 1998)
منابع مشابه
Noise Induced Escape from Different Types of Chaotic Attractor
Noise-induced escape from a quasi-attractor, and from the Lorenz attractor with non-fractal boundaries, are compared through measurements of optimal paths. It has been found that, for both types of attractor, there exists a most probable (optimal) escape trajectory, the prehistory of the escape being defined by the structure of the chaotic attractor. For a quasi-attractor the escape process is ...
متن کاملScaling in activated escape of underdamped systems.
Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents.
متن کاملPredicting Non-Stationary and Stochastic Activation of Saddle-Node Bifurcation
Accurately predicting the onset of large behavioral deviations associated with saddlenode bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and everpresent influences. As a result, it is critical to simul...
متن کاملA Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem
We consider two-dimensional overdamped double-well systems perturbed by white noise. In the weak-noise limit the most probable fluctuational path leading from either point attractor to the separatrix (the most probable escape path, or MPEP} must terminate on the saddle between the two wells. However, as the parameters of a symmetric double-well system are varied, a unique MPEP may bifurcate int...
متن کاملEscaping Saddles with Stochastic Gradients
We analyze the variance of stochastic gradients along negative curvature directions in certain nonconvex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show that contrary to the case of isotropic noise this variance is proportional to the magnitude of the corresponding eigenvalues and not decreasing in the dimensiona...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999