7,083 research outputs found
Phase Space Reconstruction from Economic Time Series Data: Improving Models of Complex Real-World Dynamic Systems
Failure of economic models to anticipate the global financial crisis illustrates the need for modeling to better capture complex real-world dynamics. Conventional models—in which economic variables evolve toward equilibria or fluctuate about equilibria in response to exogenous random shocks—are ill-equipped to portray complex real-world dynamics in which economic variables may cycle aperiodically along low-dimensional ‘strange attractors’. We present a method developed in the physics literature—‘phase space reconstruction’—that reconstructs strange attractors present in real-world dynamical systems using time series data on a single variable. Phase space reconstruction provides pictures of real-world dynamics that can guide model specificationphase space reconstruction, time series data, economic dynamics, Agribusiness, Agricultural and Food Policy, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Production Economics, Risk and Uncertainty,
Effects of additive noise on the stability of glacial cycles
It is well acknowledged that the sequence of glacial-interglacial cycles is
paced by the astronomical forcing. However, how much is the sequence robust
against natural fluctuations associated, for example, with the chaotic motions
of atmosphere and oceans? In this article, the stability of the
glacial-interglacial cycles is investigated on the basis of simple conceptual
models. Specifically, we study the influence of additive white Gaussian noise
on the sequence of the glacial cycles generated by stochastic versions of
several low-order dynamical system models proposed in the literature. In the
original deterministic case, the models exhibit different types of attractors:
a quasiperiodic attractor, a piecewise continuous attractor, strange nonchaotic
attractors, and a chaotic attractor. We show that the combination of the
quasiperiodic astronomical forcing and additive fluctuations induce a form of
temporarily quantised instability. More precisely, climate trajectories
corresponding to different noise realizations generally cluster around a small
number of stable or transiently stable trajectories present in the
deterministic system. Furthermore, these stochastic trajectories may show
sensitive dependence on very small amounts of perturbations at key times.
Consistently with the complexity of each attractor, the number of trajectories
leaking from the clusters may range from almost zero (the model with a
quasiperiodic attractor) to a significant fraction of the total (the model with
a chaotic attractor), the models with strange nonchaotic attractors being
intermediate. Finally, we discuss the implications of this investigation for
research programmes based on numerical simulators. }Comment: Parlty based on a lecture given by M. Crucifix at workshop held in
Rome in 2013 as a part of Mathematics of Planet Earth 201
Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles
Glacial-interglacial cycles are large variations in continental ice mass and
greenhouse gases, which have dominated climate variability over the Quaternary.
The dominant periodicity of the cycles is 40 kyr before the so-called
middle Pleistocene transition between 1.2 and 0.7 Myr ago, and it
is 100 kyr after the transition. In this paper, the dynamics of
glacial-interglacial cycles are investigated using a phase oscillator model
forced by the time-varying incoming solar radiation (insolation). We analyze
the bifurcations of the system and show that strange nonchaotic attractors
appear through nonsmooth saddle-node bifurcations of tori. The bifurcation
analysis indicates that mode-locking is likely to occur for the 41 kyr glacial
cycles but not likely for the 100 kyr glacial cycles. The sequence of
mode-locked 41 kyr cycles is robust to small parameter changes. However, the
sequence of 100 kyr glacial cycles can be sensitive to parameter changes when
the system has a strange nonchaotic attractor.Comment: 25 pages, 9 figure
Strange nonchaotic stars
The unprecedented light curves of the Kepler space telescope document how the
brightness of some stars pulsates at primary and secondary frequencies whose
ratios are near the golden mean, the most irrational number. A nonlinear
dynamical system driven by an irrational ratio of frequencies generically
exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we
present evidence of the first observation of strange nonchaotic dynamics in
nature outside the laboratory. This discovery could aid the classification and
detailed modeling of variable stars.Comment: 5 pages, 4 figures, published in Physical Review Letter
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