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Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth

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  • Bella, Giovanni

Abstract

This paper explores the possibility of complex dynamics in a variant of the [29] model of endogenous growth. In particular, we derive the exact parametric configuration that allows for the emergence of a double-pulse homoclinic orbit, and the rise of globally indeterminate solutions, in the same area where local determinacy was found. Our results confirm that irregular patterns and oscillating solutions can be obtained along a subsidiary homoclinic orbit at which the periodic loop starts to double, so that the system might perpetually oscillate around the long run equilibrium, being thus confined in a stationary trapping region outside the neighborhood of the steady state. The economic implications of these results are finally discussed.

Suggested Citation

  • Bella, Giovanni, 2017. "Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 452-460.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:452-460
    DOI: 10.1016/j.chaos.2017.08.025
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    1. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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    More about this item

    Keywords

    Romer model; Belyakov point degeneracy; Double-pulse homoclinic orbit; Global indeterminacy;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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