The existence and uniqueness of limit cycles in the Kaldor-Kalecki model of business
cycle.
Authors:
Adam Krawiec, Marek Szydlowski
In the paper it is analysed the Kaldor-Kalecki model of business cycle. The
time-to-build is introduced to the capital accumulation equation of the Kaldor model,
according to Kalecki's idea of delay in investment processes. The dynamics of this model
is represented in terms of time delay differential equation system. There are two causes
which generate cycle behaviour in the model. Apart from the Kaldor assumption of special
nonlinearity in the investment function, the cycle behaviour is due to time delay
parameter. In both scenario cyclic behaviour emerges from the Hopf bifurcation to the
periodic orbit.
We discuss a problem of existence of a global attractor in 2-dimensional phase space
which counterpart for the Kaldor model was considered by Chang and Smyth. It is shown that
the presence of time-to-build excludes the asymptotical stable global critical point.
Additionally we analyse the question of uniqueness of the limit cycles of the model. We
found that there is a possibility of several stable and unstable limit cycles and a final
state depends on initial value of phase variables.
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