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**Stability, instability and complex behavior in macrodynamic models with policy lag.**
*(English)*
Zbl 0980.34070

The authors consider simple macrodynamic models with policy lag by means of mixed difference and differential equations, and study how lags in policy response affect the macrodynamic (in)stability. Local dynamics of the prototype model are studied analytically, and the global dynamics of the prototype and the extended models are studied by means of numerical simulations. They show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system becomes locally unstable when the policy lag is too long. They also show the existence of cycles and complex behavior in some range of the policy lag.

Reviewer: Marcos Lizana (Merida)

### MSC:

34K20 | Stability theory of functional-differential equations |

34K18 | Bifurcation theory of functional-differential equations |

91B64 | Macroeconomic theory (monetary models, models of taxation) |

37N40 | Dynamical systems in optimization and economics |

37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |

34K35 | Control problems for functional-differential equations |

34H05 | Control problems involving ordinary differential equations |