This paper proposes a methodological approach to analyzing the evolution of the stability of socioeconomic systems and to assessing the risk of their possible destabilization based on the use of mathematical modeling methods. In this paper, a basic model is presented allowing us to describe the joint dynamics of processes in the economic, organizational, and sociopsychological areas of society. The model shows at what parameters of the socioeconomic system its steady functioning is possible, and at which it is impossible. It is shown that the transition from its steady state to an unsteady one is not smooth but occurs as a leap. This methodology is applied to the analysis of stability and change in the Egyptian socioeconomic system after 2010.

本文提出了一种方法论方法，用于分析社会经济系统稳定性的演变，并基于使用数学建模方法评估其可能的不稳定风险。在本文中，提出了一个基本模型，使我们能够描述社会经济、组织和社会心理学领域中过程的联合动态。该模型显示了在社会经济系统的哪些参数下，它的稳定运行是可能的，而在哪些参数下则是不可能的。结果表明，从稳定状态到不稳定状态的过渡不是平滑的，而是作为跳跃发生的。该方法用于分析 2010 年后埃及社会经济体系的稳定性和变化。