Noise-Induced Phenomena in Slow-Fast Dynamical Systems pdf epub mobi txt 电子书 下载 2025
- 数学
- 动力系统
- 噪声效应
- 慢-快动力学
- 非平衡态
- 随机动力学
- 分岔理论
- 时滞系统
- 复杂系统
- 应用数学
- 物理学
具体描述
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains. In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed. The emphasis lies on noise-induced phenomena such as stochastic resonance, hysteresis, excitability, and the reduction of bifurcation delay.
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