Two-parameter Nonlinear Wave Model for Transport Phenomena in Dynamic Systems with After-effects
Kayumova U. Mussabekov A. Brener A. Utepbergenov I. Mussabekov N.
2026World Scientific and Engineering Academy and Society
WSEAS Transactions on Fluid Mechanics
2026#211 - 6 pp.
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 systems 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 systems 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. The results of conducted researches and the novel model will nevertheless can find application in engineering practice in the design of various technological processes.
after-effects , bifurcation point , nonlinear waves , scaling , transport phenomena , Witham equation
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Auezov University of South Kazakhstan, Tauke Khan av., 5, Shymkent, Kazakhstan
Institute of Automation and Information Technologies, University of Power Engineering and Telecommunications named after Gumarbek Daukeyev, 2Baitursynuly str., 126/1, Almaty, Kazakhstan
Institute of Automation and Information Technologies, Kazakh National Research Technical University named after K.I. Satbayev, 3Satbayev str., 22, Almaty, Kazakhstan
Auezov University of South Kazakhstan
Institute of Automation and Information Technologies
Institute of Automation and Information Technologies
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