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Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System

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  • Marco Desogus

    (Department of Economics and Business Science, University of Cagliari, Via Sant’Ignazio 17, 09123 Cagliari, Italy)

  • Beatrice Venturi

    (Department of Economics and Business Science, University of Cagliari, Via Sant’Ignazio 17, 09123 Cagliari, Italy)

Abstract

Here, we discuss a three-dimensional continuous-time Lotka–Volterra dynamical system, which describes the role of government in interactions with banks and small enterprises. In Italy, during the COVID-19 emergency, the main objective of government economic intervention was to maintain the proper operation of the bank–enterprise system. We also review the effectiveness of measures introduced in response to the COVID-19 pandemic lockdowns to avoid a further credit crunch. By applying bifurcation theory to the system, we were able to produce evidence of the existence of Hopf and zero-Hopf bifurcating periodic solutions from a saddle focus in a special region of the parameter space, and we performed a numerical analysis.

Suggested Citation

  • Marco Desogus & Beatrice Venturi, 2023. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System," JRFM, MDPI, vol. 16(3), pages 1-20, March.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:3:p:171-:d:1087030
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    More about this item

    Keywords

    credit crunch; simulation; credit big data; nonlinear analysis; periodic solutions; stability; dynamical system; zero-Hopf bifurcation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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