Difference equations, such as a Ricker map, for an increased value of the parameter, experience instability of the positive equilibrium and transition to deterministic chaos. To achieve stabilization, various methods can be applied. Proportional Feedback control suggests a proportional reduction of the state variable at every $k$th step. First, if $k\ne 1$, a cycle is stabilized rather than an equilibrium. Second, the equation can incorporate an additive noise term, describing the variability of the environment, as well as multiplicative noise corresponding to possible deviations in the control intensity. The present paper deals with both issues, it justifies a possibility of getting a stable blurred $k$-cycle. Presented examples include the Ricker model, as well as equations with unbounded $f$, such as the bobwhite quail population models. Though the theoretical results justify stabilization for either multiplicative or additive noise only, numerical simulations illustrate that a blurred cycle can be stabilized when both multiplicative and additive noises are involved.

对于增加的参数值，诸如Ricker映射之类的差分方程会经历正平衡的不稳定性并过渡到确定性混沌。为了实现稳定，可以应用各种方法。比例反馈控制建议在每个$ķ$第一步。首先，如果$ķ\ne \mathrm{1个}$，周期是稳定的而不是平衡。其次，该方程式可以包含描述环境变化的加性噪声​​项，以及对应于控制强度可能偏差的乘性噪声。本文针对这两个问题，论证了使模糊变得稳定的可能性。$ķ$-周期。呈现的示例包括Ricker模型以及无界方程$F$，例如bobwhite鹌鹑种群模型。尽管理论结果证明仅对乘法噪声或加性噪声保持稳定是合理的，但数值模拟表明，当涉及乘法噪声和加性噪声时，模糊周期可以稳定。