论文标题
国家依赖噪声与特定分布的全球稳定和破坏稳定
Global stabilization and destabilization by the state dependent noise with particular distributions
论文作者
论文摘要
在自然假设下，差异方程的不稳定平衡可以通过有界的乘法噪声稳定，在每个步骤上分布着相同的分布。这包括稳定摇杆，逻辑和贝弗顿 - 荷尔特图的不稳定正平衡。引入乘法噪声还可以使所有解决方案都远离这一点的意义，从而使稳定的平衡不稳定。在我们的示例中，噪声具有对称，离散或连续的分布，并带有支持$ [-1,1] $，包括Bernoulli和均匀的连续分布。在每种情况下，我们都会获得噪声幅度的条件，以使平衡稳定或破坏稳定。计算机模拟说明了我们的结果。
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.
