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Hopf Bifurcation in a Cobweb Model with Discrete Time Delays

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  • Luca Gori
  • Luca Guerrini
  • Mauro Sodini

Abstract

We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.

Suggested Citation

  • Luca Gori & Luca Guerrini & Mauro Sodini, 2014. "Hopf Bifurcation in a Cobweb Model with Discrete Time Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, June.
    • Handle: RePEc:hin:jnddns:137090
    DOI: 10.1155/2014/137090
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    References listed on IDEAS

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    Cited by:

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    3. Dieci, Roberto & Mignot, Sarah & Westerhoff, Frank, 2022. "Production delays, technology choice and cyclical cobweb dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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