TY - JOUR
T1 - The business cycle model with a unique stable limit cycle
AU - Sasakura, Kazuyuki
PY - 1996
Y1 - 1996
N2 - This paper provides the mathematical foundation to the long-standing academic belief that Goodwin's 1951 nonlinear business cycle model has a unique stable limit cycle. In spite of the asymmetric nonlinearity of investment function, the model has certainly a unique stable limit cycle in an economically meaningful region. Once solution paths start from any initial point in the region, they all tend to the limit cycle without escaping from the region or hitting the ceiling or floor of investment during a transition period. The structural stability of the model prevents the limit cycle from vanishing in the face of small perturbations.
AB - This paper provides the mathematical foundation to the long-standing academic belief that Goodwin's 1951 nonlinear business cycle model has a unique stable limit cycle. In spite of the asymmetric nonlinearity of investment function, the model has certainly a unique stable limit cycle in an economically meaningful region. Once solution paths start from any initial point in the region, they all tend to the limit cycle without escaping from the region or hitting the ceiling or floor of investment during a transition period. The structural stability of the model prevents the limit cycle from vanishing in the face of small perturbations.
KW - Asymmetric rayleigh-type equation
KW - Goodwin's 1951 model
KW - Structural stability
KW - Unique stable limit cycle
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U2 - 10.1016/0165-1889(95)00897-7
DO - 10.1016/0165-1889(95)00897-7
M3 - Article
AN - SCOPUS:0030240772
VL - 20
SP - 1763
EP - 1773
JO - Journal of Economic Dynamics and Control
JF - Journal of Economic Dynamics and Control
SN - 0165-1889
IS - 9-10
ER -