具有特殊分布的状态相关噪声的全局镇定与失稳
Global stabilization and destabilization by the state dependent noise with particular distributions
摘要：
在自然假设下，差分方程的不稳定平衡点可以被有界乘性噪声镇定，该噪声在每一步都是同分布的。这包括Ricker、Logistic和Beverton-Holt映射的不稳定正平衡的稳定化。引入乘性噪声也可以破坏稳定的平衡，在某种意义上说，所有的解决方案都远离这一点，几乎肯定。在我们的示例中，噪声具有对称的、离散的或连续的分布，支持$[-1,1]$，包括伯努利分布和均匀连续分布。我们得到的条件，在每种情况下，允许稳定或不稳定的平衡的噪声幅度。计算机模拟说明了我们的结果。
英文摘要：
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium of Ricker, logistic, and Beverton-Holt maps. Introduction of a multiplicative noise also allows to destabilize a stable equilibrium in a sense that all solutions stay away from this point, almost surely. In our examples a noise has symmetric, discrete or continuous, distribution with support $[-1,1]$, including Bernoulli and uniform continuous distribution. We obtain conditions on the noise amplitudes in each case that allow to either stabilize or destabilize an equilibrium. Computer simulations illustrate our results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
