NONE 20260109125200165 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON FLUID MECHANICS 1790-5087 2224-347X Umida Kayumova Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent, KAZAKHSTAN Akhmetbek Mussabekov Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent, KAZAKHSTAN Arnold Brener Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent, KAZAKHSTAN Irbulat Utepbergenov Institute of Automation and Information Technologies, University of Power Engineering and Telecommunications named after Gumarbek Daukeyev, 2Baitursynuly str., 126/1, Almaty, KAZAKHSTAN Nazarbek Mussabekov Institute of Automation and Information Technologies, Kazakh National Research Technical University named after K.I. Satbayev, 3Satbayev str., 22, Almaty, KAZAKHSTAN Complex dynamic systems are characterized by the presence of memory effects and a multi-level hierarchy of relaxation times at various stages of transport processes. Therefore, reliable models of transport phenomena in such systems necessarily include a nonlocality factor due to the aftereffects of disturbances at different time stages of the process. At the same time, control parameters in models describing such dynamic systems can also change at different rates over different time intervals under the influence of external influences and relaxation processes that alter the system's structure. This factor is not always taken into account when constructing a process model. In this paper, a new heuristic model for accounting the impact of disturbances on the model structure and the appropriate control equation for describing the memory effects and the changes in the system's dynamic characteristics have been submitted. The novelty of the approach lies in the new concept for building the model, according to which the manifestation of after-effects can be caused by the memory effects formed, in turns, as a result of a change in the depth of potential wells corresponding to the stationary states of the system during the model process. Such an approach provides mathematical tools for studying bifurcation phenomena in a dynamic system described by a two-parameter model. The details of the new concept and the scheme for deriving the control equation are given. This article is theoretical in nature; the concept is based on general physical considerations. 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