By Abraham C.-L. Chian
Monetary structures show complicated dynamics evidenced through large-amplitude and aperiodic fluctuations in fiscal variables, corresponding to foreign currencies premiums and inventory industry costs, indicating that those structures are pushed faraway from the equilibrium. Characterization of the complicated habit of financial cycles, through picking usual and abnormal styles and regime switching in fiscal time sequence, is the most important for trend reputation and forecasting of monetary cycles. Statistical research of inventory markets and foreign currency markets has established the intermittent nature of monetary time sequence. A nonlinear version of industrial cycles is ready to simulate intermittency coming up from order-chaos and chaos-chaos transitions. This monograph introduces new options of risky periodic orbits and chaotic saddles that are volatile constructions embedded in a chaotic attractor, chargeable for fiscal intermittency.
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Additional info for Complex Systems Approach to Economic Dynamics
Nonlinear evolution of economic instabilities leads to large-amplitude ﬂuctuations of business cycles due to trajectories far-from-equilibrium. Complex systems approach provides a powerful tool to monitor and forecast the nonlinear dynamics of business cycles. For example, Mosekilde et al. (1992) studied the nonlinear mode-interaction between long-term and short-term business cycles; in a model of the economic long wave (Kondratiev cycle) driven by a periodic external forcing representing short-term business cycles, they identiﬁed nonlinear phenomena such as mode-locking, co-existence of attractors, period-doubling route to chaos, intermittent route to chaos, and crisis.
6. Poincar´e map in the vicinity of CA1 (same region as Fig. 2(b)). 98766). The crosses denote the Poincar´e points of the mediating unstable periodic orbit of period-3; the dark lines (dark points) denote the chaotic attractors (CA1 and MCA); the light lines denote the stable/unstable manifolds (SM/UM) of the mediating saddle. 1(c). 1 shows that there are many chaotic regions within a periodic window and there are many periodic windows within a 58 5 Attractor Merging Crisis in Nonlinear Economic Cycles MCA MC a CA1 /CA2 SNB SNB M1 M2 SNB A1 SNB A2 Fig.
We will show that following the onset of an attractor merging crisis, the economic system retains its memory of the weakly chaotic dynamics before the crisis; as a result, the time series of business cycles becomes intermittent displaying episodic regime switching between periods of weakly and strongly chaotic ﬂuctuations. 2. 3. 4. 2 Nonlinear Model of Economic Cycles We model the nonlinear dynamics of business cycles driven by the forced van der Pol diﬀerential equation x ¨ + μ(x2 − 1)x˙ + x = a sin(ωt).
Complex Systems Approach to Economic Dynamics by Abraham C.-L. Chian