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Dynamics of a tourism sustainability model with distributed delay

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  • Kaslik, Eva
  • Neamţu, Mihaela

Abstract

This paper generalizes the existing minimal mathematical model of a given generic touristic site by including a distributed time-delay to reflect the whole past history of the number of tourists in their influence on the environment and capital flow. A stability and bifurcation analysis is carried out on the coexisting equilibria of the model, with special emphasis on the positive equilibrium. Considering general delay kernels and choosing the average time-delay as bifurcation parameter, a Hopf bifurcation analysis is undertaken in the neighborhood of the positive equilibrium. This leads to the theoretical characterization of the critical values of the average time delay which are responsible for the occurrence of oscillatory behavior in the system. Extensive numerical simulations are also presented, where the influence of the investment rate and competition parameter on the qualitative behavior of the system in a neighborhood of the positive equilibrium is also discussed.

Suggested Citation

  • Kaslik, Eva & Neamţu, Mihaela, 2020. "Dynamics of a tourism sustainability model with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300096
    DOI: 10.1016/j.chaos.2020.109610
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    References listed on IDEAS

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    1. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," MPRA Paper 34397, University Library of Munich, Germany.
    2. Hallegatte, Stéphane & Ghil, Michael & Dumas, Patrice & Hourcade, Jean-Charles, 2008. "Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 57-77, July.
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    5. Matsumoto, Akio & Szidarovszky, Ferenc, 2010. "Continuous Hicksian trade cycle model with consumption and investment time delays," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 95-114, July.
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    7. Lacitignola, D. & Petrosillo, I. & Cataldi, M. & Zurlini, G., 2007. "Modelling socio-ecological tourism-based systems for sustainability," Ecological Modelling, Elsevier, vol. 206(1), pages 191-204.
    8. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    9. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.
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    Cited by:

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