Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.

Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Youth cultures, style and education

If our only sources of information were the newspapers and the television, the available evidence would suggest that youth is a terrible problem. Not only would we be convinced that most crime is committed by the social category of youth, but that young people are running out of control, that the streets are no longer safe, that all manner of standards are dropping, that the schools are in chaos, and that, as a consequence of these facts, society faces ruin. Fortunately, there is a considerable body of academic literature which rebuts these assertions, and via a more rigorous and objective analysis of society, it has sought to explain the practices, cultures and circumstances through and by which contemporary youth is formed.

Banded spatiotemporal chaos in sheared nematogenic fluids

We present the results of a numerical study of a model of the hydrodynamics of a sheared nematogenic fluid, taking into account the effects of order-parameter stresses on the velocity profile but allowing spatial variations only in the gradient direction. When parameter values are such that the stress from orientational distortions is comparable to the bare viscous stress, the system exhibits steady states with the characteristics of shear banding. In addition, nonlinearity in the coupling of extensional flow to orientation leads to the appearance of a new steady state in which the features of both spatiotemporal chaos and shear banding are present.

Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

The precision with which single cells of Dictyostelium discoideum can locate a source of cyclic AMP

When stimulated by a point source of cyclic AMP, a starved amoeba of Dictyostelium discoideum responds by putting out a hollow balloon-like membrane extension followed by a pseudopod. The effect of the stimulus is to influence the position where either of these protrusions is made on the cell rather than to cause them to be made. Because the pseudopod forms perpendicular to the cell surface, its location is a measure of the precision with which the cell can locate the cAMP source. Cells beyond 1 h of starvation respond non-randomly with a precision that improves steadily thereafter. A cell that is starved for 1-2 h can locate the source accurately 43% of the time; and if starved for 6-7 h, 87% of the time. The response always has a high scatter; population-level heterogeneity reflects stochasticity in single cell behaviour. From the angular distribution of the response its maximum information content is estimated to be 2-3 bits. In summary, we quantitatively demonstrate the stochastic nature of the directional response and the increase in its accuracy over time.

Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Proceedings of the Workshop on the Okhotsk Sea and Adjacent Areas [Vladivostok, June 1995]

I REPORT OF THE PICES WORKSHOP ON THE OKHOTSK SEA AND ADJACENT AREAS (pdf, 0.1 Mb) 1. Outline of the workshop 2. Summary reports from sessions 3. Recommendations of the workshop 4. Acknowledgments II SCIENTIFIC PAPERS SUBMITTED FROM SESSIONS 1. Physical Oceanography Sessions (pdf, 4 Mb) A. Circulation and water mass structure of the Okhotsk Sea and Northwestern Pacific Valentina D. Budaeva & Vyacheslav G. Makarov Seasonal variability of the pycnocline in La Perouse Strait and Aniva Gulf Valentina D. Budaeva & Vyacheslav G. Makarov Modeling of the typical water circulations in the La Perouse Strait and Aniva Gulf region Nina A. Dashko, Sergey M. Varlamov, Young-Ho Han & Young-Seup Kim Anticyclogenesis over the Okhotsk Sea and its influence on weather Boris S. Dyakov, Alexander A. Nikitin & Vadim P. Pavlychev Research of water structure and dynamics in the Okhotsk Sea and adjacent Pacific Howard J. Freeland, Alexander S. Bychkov, C.S. Wong, Frank A. Whitney & Gennady I. Yurasov The Ohkotsk Sea component of Pacific Intermediate Water Emil E. Herbeck, Anatoly I. Alexanin, Igor A. Gontcharenko, Igor I. Gorin, Yury V. Naumkin & Yury G. Proshjants Some experience of the satellite environmental support of marine expeditions at the Far East Seas Alexander A. Karnaukhov The tidal influence on the Sakhalin shelf hydrology Yasuhiro Kawasaki On the formation process of the subsurface mixed water around the Central Kuril Islands Lloyd D. Keigwin Northwest Pacific paleohydrography Talgat R. Kilmatov Physical mechanisms for the North Pacific Intermediate Water formation Vladimir A. Luchin Water masses in the Okhotsk Sea Andrey V. Martynov, Elena N. Golubeva & Victor I. Kuzin Numerical experiments with finite element model of the Okhotsk Sea circulation Nikolay A. Maximenko, Anatoly I. Kharlamov & Raissa I. Gouskina Structure of Intermediate Water layer in the Northwest Pacific Nikolay A. Maximenko & Andrey Yu. Shcherbina Fine-structure of the North Pacific Intermediate Water layer Renat D. Medjitov & Boris I. Reznikov An experimental study of water transport through the Straits of Okhotsk Sea by electromagnetic method Valentina V. Moroz Oceanological zoning of the Kuril Islands area in the spring-summer period Yutaka Nagata Note on the salinity balance in the Okhotsk Sea Alexander D. Nelezin Variability of the Kuroshio Front in 1965-1991 Vladimir I. Ponomarev, Evgeny P. Varlaty & Mikhail Yu. Cheranyev An experimental study of currents in the near-Kuril region of the Pacific Ocean and in the Okhotsk Sea Stephen C. Riser, Gennady I. Yurasov & Mark J. Warner Hydrographic and tracer measurements of the water mass structure and transport in the Okhotsk Sea in early spring Konstantin A. Rogachev & Andrey V. Verkhunov Circulation and water mass structure in the southern Okhotsk Sea, as observed in summer, 1994 Lynne D. Talley North Pacific Intermediate Water formation and the role of the Okhotsk Sea Anatoly S. Vasiliev & Fedor F. Khrapchenkov Seasonal variability of integral water circulation in the Okhotsk Sea B. Sea ice and its relation to circulation and climate V.P. Gavrilo, G.A. Lebedev & A.P. Polyakov Acoustic methods in sea ice dynamics studies Nina M. Pestereva & Larisa A. Starodubtseva The role of the Far-East atmospheric circulation in the formation of the ice cover in the Okhotsk Sea Yoshihiko Sekine Anomalous Oyashio intrusion and its teleconnection with Subarctic North Pacific circulation, sea ice of the Okhotsk Sea and air temperature of the northern Asian continent C. Waves and tides Vladimir A. Luchin Characteristics of the tidal motions in the Kuril Straits George V. Shevtchenko On seasonal variability of tidal constants in the northwestern part of the Okhotsk Sea D. Physical oceanography of the Japan Sea/East Sea Mikhail A. Danchenkov, Kuh Kim, Igor A. Goncharenko & Young-Gyu Kim A “chimney” of cold salt waters near Vladivostok Christopher N.K. Mooers & Hee Sook Kang Preliminary results from a numerical circulation model of the Japan Sea Lev P. Yakunin Influence of ice production on the deep water formation in the Japan Sea 2. Fisheries and Biology Sessions (pdf, 2.8 Mb) A. Communities of the Okhotsk Sea and adjacent waters: composition, structure and dynamics Lubov A. Balkonskaya Exogenous succession of the southwestern Sakhalin algal communities Tatyana A. Belan, Yelena V. Oleynik, Alexander V. Tkalin & Tat’yana S. Lishavskaya Characteristics of pelagic and benthic communities on the North Sakhalin Island shelf Lev N. Bocharov & Vladimir K. Ozyorin Fishery and oceanographic database of Okhotsk Sea Victor V. Lapko Interannual dynamics of the epipelagic ichthyocen structure in the Okhotsk Sea Valentina I. Lapshina Quantitative seasonal and year-to-year changes of phytoplankton in the Okhotsk Sea and off Kuril area of the Pacific Lyudmila N. Luchsheva Biological productivity in anomalous mercury conditions (northern part of Okhotsk Sea) Inna A. Nemirovskaya Origin of hydrocarbons in the ecosystems of coastal region of the Okhotsk Sea Tatyana A. Shatilina Elements of the Pacific South Kuril area ecosystem Vyacheslav P. Shuntov & Yelena P. Dulepova Biota of the Okhotsk Sea: Structure of communities, the interannual dynamics and current status B. Abundance, distribution, dynamics of the common fishes of the Okhotsk Sea Yuri P. Diakov Influence of some abiotic factors on spatial population dynamics of the West Kamchatka flounders (Pleuronectidae) Gordon A. McFarlane, Richard J. Beamish & Larisa M. Zverkova An examination of age estimates of walleye pollock (Theragra chalcogramma) from the Sea of Okhotsk using the burnt otolith method and implications for stock assessment and management Larisa P. Nikolenko Migration of Greenland turbot (Reinhardtius hippoglossoides) in the Okhotsk Sea Galina M. Pushnikova Fisheries impact on the Sakhalin-Hokkaido herring population Vidar G. Wespestad Is pollock overfished? C. Salmon of the Okhotsk Sea: biology, abundance and stock identification Vladimir A. Belyaev, Alexander Yu. Zhigalin Epipelagic Far Eastern sardine of the Okhotsk Sea Yuri E. Bregman, Victor V. Pushnikov, Lyudmila G. Sedova & Vladimir Ph. Ivanov A preliminary report on stock status and productive capacity of horsehair crab Erimacrus isenbeckii (Brandt) in the South Kuril Strait Natalia T. Dolganova Mezoplankton distribution in the West Japan Sea Vladimir V. Efremov, Richard L. Wilmot, Christine M. Kondzela, Natalia V. Varnavskaya, Sharon L. Hawkins & Maria E. Malinina Application of pink and chum salmon genetic baseline to fishery management Vyacheslav N. Ivankov & Valentina V. Andreyeva Strategy for culture, breeding and numerous dynamics of Sakhalin salmon populations Alla M. Kovalevskaya, Natalia I. Savelyeva & Dmitry M. Polyakov Primary production in Sakhalin shelf waters Tatyana N. Krupnova Some reasons for resource reduction of Laminaria japonica (Primorye region) Lyudmila N. Luchsheva & Anatoliy I. Botsul Mercury in bottom sediments of the northeastern Okhotsk Sea Pavel A. Luk’yanov, Natalia I. Belogortseva, Alexander A. Bulgakov, Alexander A. Kurika & Olga D. Novikova Lectins and glycosidases from marine macro and micro-organisms of Japan and Okhotsk Seas Boris A. Malyarchuk, Olga A. Radchenko, Miroslava V. Derenko, Andrey G. Lapinski & Leonid L. Solovenchuk PCR-fingerprinting of mitochondrial genome of chum salmon, Oncorhynchus keta Alexander A. Mikheev Chaos and relaxation in dynamics of the pink salmon (Oncorhynchus gorbuscha) returns for two regions Yuri A. Mitrofanov & Larisa N. Lesnikova Fish-culture of Pacific Salmons increases the number of heredity defects Larisa P. Nikolenko Abundance of young halibut along the West Kamchatka shelf in 1982-1992 Sergey A. Nizyaev Living conditions of golden king crab Lithodes aequispina in the Okhotsk Sea and near the Kuril Islands Ludmila A. Pozdnyakova & Alla V. Silina Settlements of Japanese scallop in Reid Pallada Bay (Sea of Japan) Galina M. Pushnikova Features of the Southwest Okhotsk Sea herring Vladimir I. Radchenko & Igor I. Glebov Present state of the Okhotsk herring stock and fisheries outlook Alla V. Silina & Ida I. Ovsyannikova Distribution of the barnacle Balanus rostratus eurostratus near the coasts of Primorye (Sea of Japan) Galina I. Victorovskaya Dependence of urchin Strongylocentrotus intermedius reproduction on water temperature Anatoly F. Volkov, Alexander Y. Efimkin & Valery I. Chuchukalo Feeding habits of Pacific salmon in the Sea of Okhotsk and in the Pacific waters of Kuril Islands in summer 1993 Larisa M. Zverkova & Georgy A. Oktyabrsky Okhotsk Sea walleye pollock stock status Tatyana N. Zvyagintseva, Elena V. Sundukova, Natalia M. Shevchenko & Ludmila A. Elyakova Water soluble polysaccharides of some Far-Eastern seaweeds 3. Biodiversity Program (pdf, 0.2 Mb) A. Biodiversity of island ecosystems and seasides of the North Pacific Larissa A. Gayko Productivity of Japanese scallop Patinopecten yessoensis (IAY) culture in Posieta Bay (Sea of Japan) III APPENDICES 1. List of acronyms 2. List of participants (Document pdf contains 431 pages)

Community structure in real-world networks from a non-parametrical synchronization-based dynamical approach

[EN]This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic Rössler oscillators each one characterized by a defined natural frequency, and coupled according to a predefined network topology. The interaction scheme contemplates an uniformly increasing coupling force to simulate a society in which the association between the agents grows in time. To enhance the stability of the correlated states that could emerge from the synchronization process, we propose a parameterless mechanism that adapts the characteristic frequencies of coupled oscillators according to a dynamic connectivity matrix deduced from correlated data. We show that the characteristic frequency vector that results from the adaptation mechanism reveals the underlying community structure present in the network.