The state-of-art research in the field of life’s organization confronts the need to investigate a number of interacting components, their properties and conditions of sustainable behaviour within a natural system. In biology, ecology and life sciences, the performance of such stable system is usually related to homeostasis, a property of the system to actively regulate its state within a certain allowable limits. In our previous work, we proposed a deterministic model for systems’ homeostasis. The model was based on dynamical system’s theory and pairwise relationships of competition, amensalism and antagonism taken from theoretical biology and ecology. However, the present paper proposes a different dimension to our previous results based on the same model. In this paper, we introduce the influence of inter-component relationships in a system, wherein the impact is characterized by direction (neutral, positive, or negative) as well as its (absolute) value, or strength. This makes the model stochastic which, in our opinion, is more consistent with real-world elements affected by various random factors. The case study includes two examples from areas of hydrobiology and medicine. The models acquired for these cases enabled us to propose a convincing explanation for corresponding phenomena identified by different types of natural systems.

中文翻译：

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动力系统的描述性建模和不同生命组织层次反馈稳态的确定

生命组织领域的最新研究面临着调查自然系统内许多相互作用的组成部分、它们的特性和可持续行为条件的需要。在生物学、生态学和生命科学中，这种稳定系统的性能通常与稳态有关，稳态是系统在一定允许范围内主动调节其状态的特性。在我们之前的工作中，我们提出了系统稳态的确定性模型。该模型基于动力系统理论以及从理论生物学和生态学中提取的竞争、反胃和对抗的成对关系。然而，本文提出了与我们之前基于相同模型的结果不同的维度。在本文中，我们介绍了系统中组件间关系的影响，其中，影响的特征在于方向（中性、正面或负面）及其（绝对）值或强度。这使得模型具有随机性，在我们看来，它更符合受各种随机因素影响的现实世界元素。案例研究包括来自水生物学和医学领域的两个例子。为这些案例获得的模型使我们能够对不同类型的自然系统识别出的相应现象提出令人信服的解释。