Onset of Collective Oscillation in Chemical Turbulence under Global Feedback

Preceding the complete suppression of chemical turbulence by means of global feedback, a different universal type of transition, which is characterized by the emergence of small-amplitude collective oscillation with strong turbulent background, is shown to occur at much weaker feedback intensity. We illustrate this fact numerically in combination with a phenomenological argument based on the complex Ginzburg-Landau equation with global feedback.Comment: 6 pages, 8 figures; to appear in Phys. Rev.

Cellular Structures in Catalytic Reactions with Global Coupling

By employing mirror electron microscopy (MEM) to image the Pt(110) surface during the catalytic oxidation of CO we observe that a fine cellular structure (typical dimension 1–5 μm) develops under conditions at which rate oscillations occur. Based on an analysis using the complex Ginzburg-Landau equation, it is demonstrated that such a structure forms generally in an oscillatory medium in the presence of global coupling

Controlling extended systems with spatially filtered, time-delayed feedback

We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling wave state exists, but is a member of a nowhere stable family. Our scheme stabilizes this state, and directs the system towards it from realistic, distant and noisy initial conditions. As confirmed by numerical simulation, a linear stability analysis about the controlled state accurately predicts when the scheme is successful, and illustrates some key features of the control including the individual merit of, and interplay between, the spatial and temporal degrees of freedom in the control.Comment: 9 pages REVTeX including 7 PostScript figures. To appear in Physical Review

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure

Mutual synchronization and clustering in randomly coupled chaotic dynamical networks

We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture of the couplings is responsible for the cluster structure observed. We analyse the different phases of the system and use various correlation measures in order to detect ordered non-synchronized states. Finally, it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs.Comment: 13 pages, to appear in Phys. Rev.

Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE http://pre.aps.or

Inverse bifurcation analysis: application to simple gene systems

BACKGROUND: Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. RESULTS: We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved

Парагенез активных разломов и позднекайнозойское напряженное состояние земной коры центральной части Монголии

Active faults of the Hangay-Hentiy tectonic saddle region in Central Mongolia are studied by space images interpretation, relief analysis, structural methods and tectonic stress reconstruction. The study results show that faults activation during the Late Cenozoic stage was selective, and a cluster pattern of active faults is typical for the study region. Morphological and genetic types and the kinematics of faults in the Hangay-Hentiy saddle region are related the direction of the ancient inherited structural heterogeneities. Latitudinal and WNW trending faults are left lateral strike-slips with reverse or thrust component (Dzhargalantgol and North Burd faults). NW trending faults are reverse faults or thrusts with left lateral horizontal component. NNW trending faults have right lateral horizontal component. The horizontal component of the displacements, as a rule, exceeds the vertical one. Brittle deformations in fault zones do not conform with the Pliocene and, for the most part, Pleistocene topography. With some caution it may be concluded that the last phase of revitalization of strike slip and reverse movements along the faults commenced in the Late Pleistocene. NE trending disjunctives are normal faults distributed mainly within the Hangay uplift. Their features are more early activation within the Late Cenozoic and the lack of relation to large linear structures of the previous tectonic stages. According to the stress tensor reconstructions of the last phase of deformation in zones of active faults of the Hangay-Hentiy saddle using data on tectonic fractures and fault displacements, it is revealed that conditions of compression and strike-slip with NNE direction of the axis of maximum compression were dominant. Stress tensors of extensional type with NNW direction of minimum compression are reconstructed for the Orkhon graben. It is concluded that the activation of faults in Central Mongolia in the Pleistocene-Holocene, as well as modern seismicity were controlled mainly by additional horizontal compression in the SW direction, which was associated with convergence of the Indian subcontinent and Eurasia. The influence of the asthenosphere flow in the SE direction at the base lithosphere is an additional factor facilitating strike-slip deformation of the crust in the study area and a possible explanation of divergent movements in the Baikal Rift, as well as the SE movement of the Amur plate. The Eastern Hangay crust is deformed under extension associated with a dynamic impact of the local mantle anomaly on the lithosphere. The boundary between the Amur plate and the Mongolian block (according to [Zonenshain, Savostin, 1979]) is fragmentary expressed in the tectonic structure. It represents a rim part of the deformation zone, embracing the Mongolian block and the adjacent uplifts of the Mongolian Altai, Tuva and Eastern Sayan. Along the boundary, compressive and transpressive strain occurred in the Pleistocene-Holocene.В пределах Хангай-Хэнтейской тектонической седловины в центральной части Монголии выполнены исследования активных разломов с применением дешифрирования космических снимков, анализа рельефа, геолого-структурных данных и реконструкции тектонических палеонапряжений. Показано, что активизация разломов на позднекайнозойском этапе происходила селективно и для района характерен кластерный тип локализации комплекса активных разломов. Кинематика разломов Хангай-Хэнтейской седловины и их морфолого-генетический тип связаны с простиранием наследуемой ими древней структурной неоднородности. Разломы широтного и ЗСЗ простирания являются левосторонними сдвигами при обязательном наличии взбросовой или надвиговой компоненты (Джаргалантгольский и Северо-Бурдский разломы). Разломы СЗ простирания являются взбросами или надвигами с левосторонней, а при отклонении к северу – правосторонней компонентой горизонтальных смещений (Тухмийннуур-Уртынгольский, Орхон-Сангийндалайнуурский и Ховрийнгол-Шарлийнгийнгольский разломы). Горизонтальная составляющая смещений, как правило, превышает вертикальную. Разрывные деформации в зонах разломов не конформны плиоценовому и, по большей части, плейстоценовому рельефу. С определенной долей осторожности можно заключить, что начало последнего этапа активизации сдвиговых и взбросовых движений по разломам относится к позднему плейстоцену. Разломы СВ простирания – сбросы, распространенные главным образом в пределах Хангайского поднятия. Их особенностями является более ранняя активизация в пределах позднего кайнозоя и отсутствие связи с крупными линейными структурами предыдущих тектонических этапов. Реконструкции стресс-тензоров последнего этапа деформаций в зонах активных разломов Хангай-Хэнтейской седловины по тектонической трещиноватости и смещениям по разрывам указывают на преобладание условий сжатия и сдвига с ССВ направлением оси максимального сжатия. В пределах Орхонского грабена реконструированы тензоры типа растяжения с ССЗ направлением оси минимального сжатия. Сделан вывод о том, что активизация разломов центральной части Монголии на плейстоцен-голоценовом этапе, а также современная сейсмичность контролируются в основном дополнительным горизонтальным сжатием в СВ направлении, связанным с процессом конвергенции Индостана и Евразии. Дополнительным фактором, позволяющим реализоваться сдвиговым деформациям в земной коре территории исследований и объясняющим дивергентные движения в Байкальском рифте, а также ЮВ движение Амурской плиты, является воздействие на подошву литосферы астеносферного потока в ЮВ направлении. Земная кора Восточного Хангая деформируется в условиях растяжения, которое связано с динамическим воздействием на литосферу локальной аномалии разуплотненного мантийного вещества. Граница между Амурской плитой и Монгольским блоком (по [Zonenshain, Savostin, 1979]) в тектонической структуре выражена фрагментарно и представляет собой краевую часть зоны деформаций, охватывающей Монгольский блок и прилегающие к нему поднятия Монгольского Алтая, Тувинского нагорья, Восточного Саяна. Вдоль границы на плейстоцен-голоценовом этапе реализуются деформации сжатия и транспрессии