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Dynamics analysis of a class of delayed economic model. (English) Zbl 1273.91314

Summary: This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form \(\text{d}^2p(t)/\text{d}t^2 = -\mu\delta(p(t))(\text{d}p(t)/\text{d}t) - \mu bp(t - \tau_1) - \mu(a_0p(t - \tau_2)/(a_1 + p(t - \tau_2))) + \mu(d_0 - g_0)\). At appropriate parameter values, linear stability and Hopf bifurcation including its direction and stability of the economic model are obtained. The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Our results extend and complement some earlier publications.

MSC:

91B55 Economic dynamics
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
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