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Local and global bifurcations in a model of the economic long wave
Author(s) -
Brøns Morten,
Sturis Jeppe
Publication year - 1991
Publication title -
system dynamics review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 57
eISSN - 1099-1727
pISSN - 0883-7066
DOI - 10.1002/sdr.4260070104
Subject(s) - bifurcation diagram , homoclinic bifurcation , hopf bifurcation , transcritical bifurcation , biological applications of bifurcation theory , bogdanov–takens bifurcation , infinite period bifurcation , saddle node bifurcation , mathematics , period doubling bifurcation , pitchfork bifurcation , bifurcation , bifurcation theory , limit cycle , mathematical analysis , homoclinic orbit , nonlinear system , limit (mathematics) , physics , quantum mechanics
Combining mathematical analysis with simulations, we obtain a bifurcation diagram for a simple (two state variables) system dynamics model of the economic long wave. Previous linear analysis of the onset of oscillatory behavior (Hopf bifurcation) is extended to include nonlinear effects. It is shown that both sub‐ and supercritical Hopf bifurcation can occur. In the case of subcritical Hopf bifurcation, the system has two coexisting stable solutions, one stationary and one periodic, in a parameter interval below the bifurcation point. The importance of distinguishing between the two types of Hopf bifurcation is discussed. The model also exhibits homoclinic bifurcation to infinity for some parameter combinations: a limit cycle explodes and disappears. Finally, we discuss how the results may apply to other system dynamics models.