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• W3007421856 abstract "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 $k neq 1$, 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." @default.
• W3007421856 created "2020-03-06" @default.
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• W3007421856 date "2020-05-01" @default.
• W3007421856 modified "2023-10-18" @default.
• W3007421856 title "Stabilization of cycles for difference equations with a noisy PF control" @default.
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• W3007421856 doi "https://doi.org/10.1016/j.automatica.2020.108862" @default.
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