Stochastic Dynamics of Emotional Characteristics of Cognitive Systems

 The aim of the research is to analyze the emotional state of a person using stochastic methods and to study the dynamic characteristics of this state. The study uses statistical characteristics that are suitable for creating artificial intelligent systems, as well as for further development and design of organizational and technical systems. It is assumed that the emotional state of a person is determined by the amount of stress he experiences over a certain period of time. To account for the emotional responses of the cognitive system corresponding to the reactions of the human personality, the known results are used. In particular, to characterize the relative values of stress, the Holmes and Rahe scale was used, which contains 43 typical life situations with corresponding relative values of stress. It should be emphasized that all known results relate to time-independent stress models, and only the results of statistical processing of measurements of the impact of stress on the individual at certain time intervals are published.

Materials and methods of research are the application of the Poisson model of stress occurrence in the process of system functioning. It is assumed that stresses are those impacts that are then processed, perceived, processed, and used by the individual and the organizational and technical system that models it. The occurrence of stresses over time is modeled by point Poisson processes, and the stress of each type according to Holmes and Rahe is described by a process with the corresponding individual function of the intensity of the occurrence of points (stresses). Dynamic responses of the system are described by well-known response functions in the theory of control systems. The key parameter of the response function is the time constant, which characterizes the typical response time of the system to individual stress.

New results of the study are estimates of the average frequency of occurrence of various types of stress, which allowed us to determine the mentioned functions of the intensity of occurrence of stress in the Poisson model. This, in turn, made it possible to develop analytical relations for the relative amount of stress processed by the system for the current time. Thus, a model of the emotional state of the cognitive system (the development of the process of experiencing stress over time) is proposed in the form of a decreasing function of time with a certain time constant that characterizes the inertial properties of experiencing stress. Specific results and corresponding curves are obtained for the exponential response function of the system, which depends on the current time, times of stress occurrence, and relative stress values. In general, they correspond to the predictions of similar reactions for the individual obtained in published studies. In this regard, the model can be applied in the engineering design of organizational and technical systems that require accounting or modeling of emotional reactions.

In conclusion, the directions of further development of the theory are indicated. In particular, the possibility of studying the reaction of the system to events, the occurrence of which is described by functions of the intensity of their occurrence, depending on time, which, of course, will bring the research results closer to real situations. Another important area may be the introduction of indicators and criteria for stress tolerance of systems to the consideration and study of behavior.

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