Thomsen, Jesper Skovhus with Erik Mosekilde, Erik Reimer Larsen and John D. Sterman, "Mode-Locking and Chaos in a Periodically Driven Model of the Economic Long Wave", 1990

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We have investigated the complex dynamic phenomena, which arise when the economic long wave model is perturbed by a sinusoidal variation in the orders for capital to the goods sector. The modulation represents a coupling to more short term oscillatory modes in the macroeconomic system. As the period of the external forcing is changed, a devil’s staircase of frequency -locked oscillations develops. For higher amplitudes of the perturbing signal, period-doubling bifurcations, simultaneously existing periodic solutions and deterministic chaos can be observed. The distribution of modes is determined as a function of the frequency and amplitude of the external signal. The phase diagram reveals characteristic bumps on the Arnol’d tongues, where they approach each other. The Lyapunov exponents are calculated, and the influence of noise is discussed in terms of the lock-in time for the periodic solutions.

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  • 1990
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