TITLE:
Goodwin Accelerator Model Revisited with Piecewise Linear Delay Investment
AUTHORS:
Akio Matsumoto, Keiko Nakayama, Ferenc Szidarovszky
KEYWORDS:
Nonlinear Accelerator, Investment Delay, Successive Integration, Smooth and Kinked Solutions, Numerical Analysis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.2,
February
28,
2018
ABSTRACT: It is
well-known that Goodwin’s nonlinear delay accelerator model can generate diverse oscillations (i.e., smooth and sawtooth oscillations).
It is, however, less-known what conditions are needed for these dynamics to
emerge. In this study, using a piecewise linear investment function, we solve
the governing delay differential equation and obtain the explicit forms of the
time trajectories. In doing so, we detect conditions for persistent
oscillations and also conditions for the birth of such cyclic dynamics.