By Abraham C.-L. Chian
Financial platforms convey complicated dynamics evidenced through large-amplitude and aperiodic fluctuations in financial variables, comparable to foreign currency echange charges and inventory industry costs, indicating that those platforms are pushed faraway from the equilibrium. Characterization of the advanced habit of financial cycles, through picking average and abnormal styles and regime switching in fiscal time sequence, is the most important for development reputation and forecasting of financial cycles. Statistical research of inventory markets and foreign currency echange markets has verified the intermittent nature of monetary time sequence. A nonlinear version of commercial cycles is ready to simulate intermittency coming up from order-chaos and chaos-chaos transitions. This monograph introduces new suggestions of volatile periodic orbits and chaotic saddles that are volatile constructions embedded in a chaotic attractor, accountable for monetary intermittency.
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Additional info for Complex Systems Approach to Economic Dynamics
3 Economic Type-I Intermittency 35 Fig. 7. Characteristic intermittency time τ as a function of the departure from aSNB , log10 τ as a function of log10 (aSNB − a) between periods of laminar (quiescent) phases and periods of bursting (turbulent) phases. 5, we identify the laminar phases (x˙ ∼ 2 and x˙ ∼ 0 in the driver cycle plots) as due to the memory eﬀect of the post saddle-node bifurcation p-1 unstable periodic orbits of A1 and A2 , respectively. 5. This implies that after the transition from order to chaos, the regime switching of intermittent business cycles becomes more frequent as the system moves farther away from the transition point.
9864085. 9 Unstable Periodic Orbit and Chaotic Attractor Unstable periodic orbits are the skeleton of a chaotic attractor because chaotic trajectories are closures of the set of unstable periodic orbits (Auerbach et al. 1987, Cvitanovic 1988). 2(b)). Hence, a chaotic trajectory is chaotic because it must weave in and around all of these unstable periodic orbits yet remain in a bounded region of state space (Hilborn 1994). Unstable periodic orbits can be numerically found by the Newton algorithm (Curry 1979).
074 is a linear ﬁt of the values of the characteristic intermittency time computed from the time series. The squares (circles) denote the computed average duration of the laminar phases related to A1 (A2 ). Note that the circles and the squares coincide most of the time, due to the symmetry of A1 and A2 . 074 . 2) This scaling formula can be used to predict the turning points, from contraction to expansion phases, of nonlinear business cycles. 4 Concluding Comments This chapter shows that after an economic system undergoes a dynamical transition from an ordered to chaotic state, intermittency appears whereby the economic activities switch episodically back and forth between periods of quiescent and bursting ﬂuctuations.
Complex Systems Approach to Economic Dynamics by Abraham C.-L. Chian