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We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles
We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization
Zimzum
(2004)
We derive a slip rate for a thrust at the central Qilian Shan mountain front by combining structural investigations, satellite imagery, topographic profiling, luminescence dating, and Be-10 exposure dating. The seismically active Zhangye thrust transects late Pleistocene alluvial fan deposits and forms a prominent north facing scarp. The fault consists of two segments that differ in orientation, scarp height, and age. A series of loess-covered terraces records the uplift history of the western thrust segment. Loess accumulation on all terraces started at 8.5 +/- 1.5 kyr and postdates terrace formation. Gravels from the highest terrace yielded a Be-10 exposure age of 90 +/- 11 kyr, which dates the onset of faulting. With a displacement of 55-60 m derived from fault scarp profiles, this yields a vertical slip rate of 0.64 +/- 0.08 mm yr(-1). Along the eastern thrust segment, three Be-10 ages from the uplifted alluvial fan constrain that faulting started at similar to31 +/- 5 kyr. Together with a displacement of 25-30 m this leads to a vertical faulting rate of 0.88 +/- 0.16 mm yr(-1). A dip estimate of 40degrees to 60degrees for the fault plane combined with lower and upper limits of similar to0.6 and similar to0.9 mm yr(-1) for the vertical slip rate gives minimum and maximum horizontal shortening rates of 0.4 and 1.1 mm yr(-1) across the Zhangye thrust. Our results are consistent with geologic and GPS constraints, which suggest that NNE directed shortening across the northeastern Tibetan Plateau is distributed on several active faults with a total shortening rate of 4 to 10 mm yr(-1)
[1] The development of topography within and erosional removal of material from an orogen exerts a primary control on its structure. We develop a model that describes the temporal development of a frontally accreting, critically growing Coulomb wedge whose topography is largely limited by bedrock fluvial incision. We present general results for arbitrary initial critical wedge geometries and investigate the temporal development of a critical wedge with no initial topography. Increasing rock erodibility and/or precipitation, decreasing mass flux accreting to the wedge front, increasing wedge sole-out depth, decreasing wedge and basal decollement overpressure, and increasing basal decollement friction lead to narrow wedges. Large power law exponent values cause the wedge geometry to quickly reach a condition in which all material accreted to the front of the wedge is removed by erosion. We apply our model to the Aconcagua fold-and-thrust belt in the central Andes of Argentina where wedge development over time is well constrained. We solve for the erosional coefficient K that is required to recreate the field-constrained wedge growth history, and these values are within the range of independently determined values in analogous rock types. Using qualitative observations of rock erodibilities within the wedge, we speculate that power law exponents of 1/3 less than or equal to m less than or equal to 0.4 and 2/3 less than or equal to n less than or equal to 1 characterize the erosional growth of the Aconcagua fold-and-thrust belt. This general model may be used to understand the development of mountain belts where orogenic wedges grow as they deform at their Coulomb failure limit
[1] Orogenic structure appears to be partially controlled by the addition to and removal of material from the mountain belt by tectonic accretion and geomorphic erosion, respectively. We developed a coupled erosion-deformation model for orogenic wedges that are in erosional steady state and deform at their Coulomb failure limit. Erosional steady state is reached when all material introduced into the wedge is removed by erosion that is limited by the rate at which rivers erode through bedrock. We found that the ultimate form of a wedge is controlled by the wedge mechanical properties, sole-out depth of the basal decollement, erosional exponents, basin geometry, and the ratio of the added material flux to the erosional constant. As this latter ratio is increased, wedge width and surface slopes increase. We applied these models to the Taiwan and Himalayan orogenic wedges and found that despite a higher flux of material entering the former, the inferred ratio was larger for the latter. Calculated values for the erodibility of each wedge showed at least an order of magnitude lower value for the Himalaya relative to Taiwan. These values are consistent with the lower precipitation regime in the Himalaya relative to Taiwan and the exposure of crystalline rocks within the Himalayan orogenic wedge. Independently determined rock erodibility estimates are consistent with the accretionary wedge sediments and metasediments and the crystalline and high-grade metamorphic rocks exposed within Taiwan and the Himalaya, respectively. Therefore differences in rock type and climate apparently lead to key differences in the erosion and hence orogenic structure of these two mountain belts
A fault scaling law suggests that, over eight orders of magnitude, fault length L is linearly related to maximum displacement D. Individual faults may therefore retain a constant ratio of D/L as they grow. If erosion is minor compared with tectonic uplift, the length and along-strike relief of young mountain ranges should thus reflect fault growth. Topographic profiles along the crests of mountain ranges in the actively deforming foreland of north-east Tibet exhibit a characteristic shape with maximum height near their centre and decreasing elevation toward the tips. We interpret the along-strike relief of these ranges to reflect the slip distribution on high-angle reverse faults. A geometric model illustrates that the lateral propagation rate of such mountain ranges may be deciphered if their length- to-height ratio has remained constant. As an application of the model, we reconstruct the growth of the Heli Shan using a long-term uplift rate of similar to1.3 mm yr(-1) derived from Ne-21 and Be-10 exposure dating
We argue that there is a crucial difference between determiner and adverbial quantification. Following Herburger [2000] and von Fintel [1994], we assume that determiner quantifiers quantify over individuals and adverbial quantifiers over eventualities. While it is usually assumed that the semantics of sentences with determiner quantifiers and those with adverbial quantifiers basically come out the same, we will show by way of new data that quantification over events is more restricted than quantification over individuals. This is because eventualities in contrast to individuals have to be located in time which is done using contextual information according to a pragmatic resolution strategy. If the contextual information and the tense information given in the respective sentence contradict each other, the sentence is uninterpretable. We conclude that this is the reason why in these cases adverbial quantification, i.e. quantification over eventualities, is impossible whereas quantification over individuals is fine.
Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved