In this study, we consider a parametric uncertain Lotka-Volterra cancer model including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The biological parameter (i.e., cell growth rate) is described as a form of the triangular fuzzy number. By using grade mean value conversion, the imprecise fuzzy parameter is translated into the degree of optimism ( λ -integral value λ ∈ [0,1]) interval. We derive the sufficient conditions for the existence of the region of asymptotic stability (RAS) in the fuzzy cancer model. The boundary crisis of transient chaos and properties of RAS are investigated under fuzzy environment. We present a dynamical perturbation control to avoid uncontrolled tumor cell growth and prevent healthy cell extinction.

中文翻译：

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参数不确定癌症系统的动态控制

在这项研究中，我们考虑了一个参数不确定的 Lotka-Volterra 癌症模型，包括三个相互作用的肿瘤细胞群、健康宿主细胞和免疫效应细胞。生物参数（即细胞生长率）被描述为三角模糊数的一种形式。通过使用等级平均值转换，将不精确的模糊参数转化为乐观度（λ-积分值λ∈[0,1]）区间。我们推导出了模糊癌症模型中渐近稳定性区域（RAS）存在的充分条件。研究了模糊环境下瞬态混沌的边界危机和RAS的性质。我们提出了一种动态扰动控制，以避免不受控制的肿瘤细胞生长并防止健康细胞灭绝。