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Modern and generalized analysis of exogenous growth models

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  • Atangana, Abdon
  • Doungmo Goufo, Emile Franc

Abstract

The work presents a critical analysis of the model that could replicate the dynamic of long-run economic growth by regarding the capital accumulation, the labor or the population growth and increases in productivity that depends on technological progress. In this case, we calculated the equilibrium point and gave the model’s existence and uniqueness conditions. We introduced an analysis of the Lyapunov function for the first and second derivatives. Infections point analysis was presented in detail, and a numerical scheme based on the Lagrange polynomial interpolation was used to derive the numerical solution of the classical model. To introduce into mathematical formulation nonlocal behaviors, four cases were considered, including the effect of the power-law, the impact of fading memory, the development of crossover from stretched exponential to power-law and crossover behaviors from power law to stochastic. For each case, Linear growth and Lipschitz conditions were used to establish the uniqueness of the exact solution. Further, different numerical techniques were used to prove convergence of the used numerical scheme. Finally, numerical simulations were performed for other cases.

Suggested Citation

  • Atangana, Abdon & Doungmo Goufo, Emile Franc, 2022. "Modern and generalized analysis of exogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007913
    DOI: 10.1016/j.chaos.2022.112605
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    References listed on IDEAS

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    1. Doungmo Goufo, Emile Franc, 2017. "Solvability of chaotic fractional systems with 3D four-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 443-451.
    2. Acemoglu, Daron, 2012. "Introduction to economic growth," Journal of Economic Theory, Elsevier, vol. 147(2), pages 545-550.
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