This paper extends the classical repeated duopoly model with quantity-setting firms of Bischi et al. (1998) by assuming that production of goods is subject to some gestation lags but exchanges take place continuously on the market. The model is expressed in the form of differential equations with discrete delays. By using some recent mathematical techniques and numerical experiments, results show some dynamic phenomena that cannot be observed when delays are absent. In addition, depending on the extent of time delays and inertia, synchronisation failure can arise even in the event of homogeneous firms.
This paper is devoted to the existence and stability analysis of limit cycles in a delayed
mathematical model for the economy growth. Specifically the Solow model is further
improved by inserting the time delay into the logistic population growth rate. Moreover,
by choosing the time delay as a bifurcation parameter, we prove that the system loses its
stability and a Hopf bifurcation occurs when time delay passes through critical values.
Finally, numerical simulations are carried out for supporting the analytical results.
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