Studying the dynamics of nonlinear interaction between enterprise populations

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The article highlights the results of a study of the dynamic evolutionary processes of trophic relations between populations of enterprises. A model based on differential equations is constructed, which describes the economic system and takes into account the dynamics of the specific income of competing populations of enterprises in relations of protocooperation, nonlinearity of growth and competition. This model can be used to analyze the dynamics of transient processes in various life cycle scenarios and predict the synergistic effect of mergers and acquisitions. A bifurcation analysis of possible scenarios of dynamic modes of merger and acquisition processes using the neural network system of pattern recognition was carried out. To this end, a Kohonen self-organizing map has been constructed, which recognizes phase portraits of bifurcation diagrams of enterprises life cycle into five separate classes in accordance with the scenarios of their development. As a result of the experimental study, characteristic modes of the evolution of economic systems were revealed, and also conclusions were made on the mechanisms of influence of the external environment and internal structure on the regime of evolution of populations of enterprises.

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    • Figure 1. Тривимірний фазовий портрет життєвого циклу розвитку підприємства
    • Figure 2. Параметричні діаграми моделі (сценарій ЖЦП «розквіт»)
    • Figure 3. Параметричні діаграми моделі (сценарій ЖЦП «летальна»)
    • Figure 4. Фазові портрети біфуркаційних діаграм моделі: сценарії ЖЦП а) летальна, б) народження, в) розвиток
    • Figure 5. Фазові портрети біфуркаційних діаграм моделі: сценарій ЖЦП а), б) зрілість
    • Figure 6. Фазові портрети біфуркаційних діаграм моделі: сценарій ЖЦП а), б), в) розквіт
    • Figure 7. Компонентні фігури вагових позицій параметрів стану біфуркації ЖЦП Підприємств
    • Figure 8. Діаграма влучень прикладів у нейрони гексагональної конфігурації
    • Figure 9. Уніфікована матриця відстаней
    • Tables 1. Дані для розпізнавання стану біфуркації ЖЦП підприємств
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Neuro-Fuzzy Modeling Techniques in Economics
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