Mathematical modeling of transient processes in hierarchical structures of public administration with nonlinear characteristics
Authors: Valery Ignatkin , Yury Shulzhyk , Volodymyr Dudnikov , Oleh Yushkevych 
Published: April 2024

The last decades are characterized by a large number of studies of state and public figures, which can be called an era of deep (fundamental) and rapid changes. Society is experiencing qualitative changes and serious challenges, therefore there is a kind of paradox when the imperatives of a new era force the development of a theoretical basis in the semantic field of common sense, which is associated with permanence and qualitative changes in political, economic and social life [1, 2, 3] . In state administration and local self-government bodies, relations between people, rapid unpredictable changes in the situation in the country and in regions (political, economic, social, etc.) are non-linear management systems. Moreover, any physical system when examined in more detail is always nonlinear. The effectiveness of managing a nonlinear system, taking into account disturbing factors, depends on the accuracy of forecasting the dynamics of changes in individual elements of such a system. This is a multifaceted problem [15]. A characteristic feature of non-linear hierarchical structures (NIS) in the public service (state administration - DU and local self-government - MS) is a continuous and discrete change in the processes of development of events, which distinguishes them from other internal and external influences, such as those that cause the transformation of linear communication into non-linear, which ultimately leads to new changes. This is the first thing. Second, subject-object relationships can have uncoordinated actions caused by real-world circumstances. Such uncoordinated actions can occur even more in transitional processes of society (for example, the speed of their flow) due to the inertia of individual elements or the social system itself as a whole. As a result of these phenomena, the linear relationship between discrete changes is broken and the previous hierarchical structure changes, which leads to non-linear information relationships in the state administration (SU) and local self-government bodies (MS). For example, G. Pocheptsov and other scientists associate this nonlinearity with chaos, the growing complexity of social processes, globalization, with a threat to state security, with the manifestation of unpredictability and instability [1-5]. Strict requirements are imposed on the management process in the new state of DU and MS: - resilience of the management system; - the system should be described as continuous-discrete (its dynamics); - the management process must ensure the necessary accuracy of matching the indicators of the new state of the system with the previous one. A number of problems appear in newly formed non-linear hierarchical structures (NIS) in DU and MS: - lack of a priori information about processes with non-linear connections; - inaccuracy of structural identification; - inaccuracy in the choice of criteria for assessing the situation; - restructuring processes; - wrong choice of states of nature; - incorrect determination of the importance of the selected criteria according to the scale of importance; - incorrectly chosen dependence of alternatives on the criterion; - insufficient degree of awareness of the complexity of the situation. Solving the above problems requires experimental research. If the process of stabilization of the NIS in the DU is considered as an object of regulation, then it is enough to establish the dependence of this stability on the control action and the main disturbance, and all other actions are considered as disturbances on the object of study. Such a description will reflect the main dynamic characteristics of such a process and will be sufficient for the synthesis and development of an optimal regulation system with the aim of achieving stable (stable) processes in such systems (including DU and MS). In the future, we will approach the DU as a non-linear hierarchical system (NHS) and depict the NIS as a multidimensional continuous system, in which the state of nature is the regulated quantity, and the input is the action of managers in the DU and MS (management decisions made by them - PUR) regarding regulation , coordination and perturbations acting on the system.