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.


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
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