Моделювання систем управління у інформаційному противоборстві на основі застосування концепції нейрофізіології, теорій гіперкомплексних чисел та хаосу

Purpose of the article. The purpose of this study is to investigate and define the conceptual foundations for an interdisciplinary synthesis of methods based on neurophysiology, cybernetics, and hypercomplex mathematics for the development of universal models of complex control systems in information confrontation. The study further aims to establish, grounded in the theory of hypercomplex dynamical systems and associative-projective structures, a framework for the practical formalisation of complex control system models with multidimensional, non-commutative interactions, enabling an adequate representation of their functioning as objects of information confrontation within a reflexive model of information conflict. Research methods. The study employs methods of systems analysis, neuromorphic modelling, hypercomplex mathematics (in particular, quaternion algebra), chaos theory, and Lyapunov’s direct method for stability assessment. The proposed methodological approach enables the formalisation of information-confrontation processes and the stability analysis of complex control systems without the need to solve the complex dynamic equations of motion of unmanned aerial vehicles. Research results. For the first time, a concept for modelling complex control systems under conditions of information conflict is proposed, integrating neurophysiological approaches, hypercomplex number theory, chaos theory, and Lyapunov functions. The approaches to formalising processes of destructive information interaction and decision-making in complex control systems have been improved. The modelling of information confrontation has been further developed through the construction of a generalised model that integrates the interaction between opposing parties with the “cognitive” model of the control system. The effectiveness of the proposed approach is validated through a case study involving the interaction between unmanned aerial vehicle control systems and electronic warfare systems. Scientific novelty. The scientific novelty of this work lies in the formalisation of information warfare processes as a nonlinear dynamic system with elements of chaotic behaviour, within which the influence of destructive factors is interpreted as a diffusive process of information energy degradation. A new approach to modelling complex control systems is proposed, based on a hypercomplex representation of states and neuromorphic associative-projective structures, enabling the integration of cognitive, informational, and technical components within a single formalised model. Theoretical and practical significance. The theoretical contribution lies in developing a unified methodological framework for modelling complex control systems at a high level of abstraction. The practical significance lies in the applicability of the proposed models for assessing the stability of control systems, enhancing the effectiveness of electronic warfare systems, and supporting the development of decision-support systems in cybersecurity and military command and control.