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Complex Systems Approach to Economic Dynamics by Abraham C.-L. Chian

By Abraham C.-L. Chian

Monetary platforms express complicated dynamics evidenced through large-amplitude and aperiodic fluctuations in financial variables, corresponding 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, by means of making a choice on normal and abnormal styles and regime switching in financial time sequence, is the main for development popularity and forecasting of financial cycles. Statistical research of inventory markets and foreign currency echange markets has tested the intermittent nature of financial time sequence. A nonlinear version of commercial cycles is ready to simulate intermittency bobbing up from order-chaos and chaos-chaos transitions. This monograph introduces new suggestions of risky periodic orbits and chaotic saddles that are volatile buildings embedded in a chaotic attractor, liable for financial intermittency.

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66 is a linear fit. The squares (circles) denote the computed average time of the laminar phases related to CA1 (CA2 ). Note that circles and squares coincide most of the time, as expected from the symmetry of CA1 and CA2 . 66 . 66 2 1 0 −6 −5 −4 −3 −2 log10( a − a MC ) Fig. 7. Characteristic intermittency time as a function of the departure from the crisis point, log10 τ versus log10 (a−aM C ). The squares (circles) denote the computed average switching time from the laminar phases related to CA1 (CA2 ) to the bursty phases.

Region, the trajectory converges to the chaotic attractor A0 ; whereas, for initial conditions starting in the dark gray (white) region, the trajectory converges to the periodic attractor A1 (A2 ), respectively. 983140, where the light gray (white) region denotes the basin of attraction for attractor A1 (A2 ). 983140. This dramatic change is due to the destruction of the chaotic attractor A0 and its basin of attraction by a boundary crisis. 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.

5(b), respectively. 5(d), respectively. 98765 CA1 2 x 0 CA2 −2 −4 716 752 788 824 driver cycles Fig. 4. 98765: (a) x(t) ˙ for chaotic attractor ˙ for chaotic attractor CA2 ; (c) x˙ as a function of driver cycles for (a) CA1 ; (b) x(t) and (b), respectively intermittent after the onset of attractor merging crisis, with periods of weakly chaotic (laminar) fluctuations interrupted abruptly by periods of strongly chaotic (bursty) fluctuations. 5 are related to the pre-crisis attractors CA1 and CA2 . Hence, the postcrisis system keeps memory of its weakly chaotic dynamics prior to crisis, and switches back and forth between the low-level fluctuations related to CA1 and CA2 , linked by high-level fluctuations related to MCA.

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