Amplitude chimeras and chimera death in dynamical networks

We find chimera states with respect to amplitude dynamics in a network of Stuart-Landau oscillators. These partially coherent and partially incoherent spatio-temporal patterns appear due to the interplay of nonlocal network topology and symmetry-breaking coupling. As the coupling range is increased, the oscillations are quenched, amplitude chimeras disappear and the network enters a symmetry-breaking stationary state. This particular regime is a novel pattern which we call chimera death. It is characterized by the coexistence of spatially coherent and incoherent inhomogeneous steady states and therefore combines the features of chimera state and oscillation death. Additionally, we show two different transition scenarios from amplitude chimera to chimera death. Moreover, for amplitude chimeras we uncover the mechanism of transition towards in-phase synchronized regime and discuss the role of initial conditions

Smoothness of Nonlinear and Non-Separable Subdivision Schemes

We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in $L^p$ and Sobolev spaces

Distant interaction of rock mass clusters around underground opening

Purpose. To experimentally prove the fact of distant interaction between rock clusters during the irreversible displacements of rock mass. Disintegration of the rock mass does not necessarily imply loss in underground working stability. Methods. Telltales were used to monitor rock mass around the underground development working in conditions of intensive rock pressure manifestation. Findings. This experiment has demonstrated that the boundary of the rock mass failure expands asynchronously by spatially and temporally discrete increments. Such mechanism of the rock failure zone development is the consequence of the minimum entropy production principle according to which dissipative structures can occur in open thermodynamic systems. Originality. Distant interaction of rock clusters has been experimentally detected for the first time, which is important for geomechanics because it reveals the mechanism of the rock mass self-organization. Practical implications. The most efficient special technologies have been selected and quantitatively assessed for the control of rock mass state in conditions of severe rock pressure manifestation.Мета. Експериментально довести наявність дальньої взаємодії породних кластерів під час необоротних зрушень масиву гірських порід. Дезінтеграція масиву гірських порід не обов’язково тягне за собою втрату стійкості підземної виробки. Методика. Використовуючи глибинні репери, здійснено моніторинг масиву гірських порід навколо підземної підготовчої виробки в умовах інтенсивного прояву гірського тиску. Результати. Даний експеримент продемонстрував, що границі зруйнованого масиву розширюються асинхронно, прирощуючи зону руйнування окремими порціями у просторі й часі. Такий механізм розвитку зони зруйнованих порід є наслідком закону про мінімум виробництва ентропії, який стверджує, що у відкритих термодинамічних системах можуть виникати дисипативні структури. Наукова новизна. Дальня взаємодія породних кластерів у масиві гірських порід була експериментально зареєстрована вперше, що є важливим у галузі геомеханіки, оскільки було підтверджено механізм самоорганізації масиву гірських порід. Практична значимість. Найбільш ефективні спеціальні технології були виявлені й кількісно оцінені для управління станом масиву гірських порід в умовах інтенсивного прояву гірського тиску.Цель. Экспериментально доказать наличие дальнего взаимодействия породных кластеров во время необратимых сдвижений массива горных пород. Дезинтеграция массива горных пород не обязательно влечет за собой потерю устойчивости подземной выработки. Методика. Используя глубинные реперы, осуществлен мониторинг массива горных пород вокруг подземной подготовительной выработки в условиях интенсивного проявления горного давления. Результаты. Данный эксперимент продемонстрировал, что границы разрушенного массива расширяются асинхронно, приращивая зону разрушения отдельными порциями в пространстве и времени. Такой механизм развития зоны разрушенных пород является следствием закона о минимуме производства энтропии, который утверждает, что в открытых термодинамических системах могут возникать диссипативные структуры. Научная новизна. Дальнее взаимодействие породных кластеров в массиве горных пород было экспериментально зарегистрировано впервые, что является важным в области геомеханики, поскольку было подтверждено механизм самоорганизации массива горных пород. Практическая значимость. Наиболее эффективные специальные технологии были выявлены и количественно оценены для управления состоянием массива горных пород в условиях интенсивного проявления горного давления.This research has been supported by the National Academy of Sciences of Ukraine (grant ІІІ-2-2017)

Time-delayed feedback control of coherence resonance chimeras

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 27, 114320 (2017) and may be found at https://doi.org/10.1063/1.5008385.Using the model of a FitzHugh-Nagumo system in the excitable regime, we investigate the influence of time-delayed feedback on noise-induced chimera states in a network with nonlocal coupling, i.e., coherence resonance chimeras. It is shown that time-delayed feedback allows for the control of the range of parameter values where these chimera states occur. Moreover, for the feedback delay close to the intrinsic period of the system, we find a novel regime which we call period-two coherence resonance chimera. Coherence resonance chimeras in nonlocally coupled networks of excitable elements represent partial synchronization patterns composed of spatially separated domains of coherent and incoherent spiking behavior, which are induced by noise. These patterns are different from classical chimera states occurring in deterministic oscillatory systems and combine properties of the counter-intuitive phenomenon of coherence resonance, i.e., a constructive role of noise, and chimera states, i.e., the coexistence of spatially synchronized and desynchronized domains in a network of identical elements. Another distinctive feature of the particular type of chimera we study here is its alternating behavior, i.e., periodic switching of the location of coherent and incoherent domains. Applying time-delayed feedback, we demonstrate how to control coherence resonance chimeras by adjusting delay time and feedback strength. In particular, we show that feedback increases the parameter intervals of existence of chimera states and has a significant impact on their alternating dynamics leading to the appearance of novel patterns, which we call period-two coherence resonance chimera. Since the dynamics of every individual network element in our study is given by the FitzHugh-Nagumo (FHN) system, which is a paradigmatic model for neurons in the excitable regime, we expect wide-range applications of our results to neural networks.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Birth and Death of Chimera: Interplay of Delay and Multiplexing

The chimera state with co-existing coherent-incoherent dynamics has recently attracted a lot of attention due to its wide applicability. We investigate non-locally coupled identical chaotic maps with delayed interactions in the multiplex network framework and find that an interplay of delay and multiplexing brings about an enhanced or suppressed appearance of chimera state depending on the distribution as well as the parity of delay values in the layers. Additionally, we report a layer chimera state with an existence of one layer displaying coherent and another layer demonstrating incoherent dynamical evolution. The rich variety of dynamical behavior demonstrated here can be used to gain further insight into the real-world networks which inherently possess such multi-layer architecture with delayed interactions

Chimera states in complex networks: interplay of fractal topology and delay

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.Comment: arXiv admin note: text overlap with arXiv:1603.0017

Chimera states and the interplay between initial conditions and non-local coupling

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 27, 033110 (2017) and may be found at https://doi.org/10.1063/1.4977866.Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are linked to the occurrence of chimera states, flipped profiles of the mean phase velocity, and the transition from a phase- to an amplitude-mediated chimera state. Chimera states are an example of intriguing partial synchronization patterns appearing in networks of identical oscillators with symmetric coupling scheme. They exhibit a hybrid structure combining coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics and were first reported for the model of phase oscillators. Recent studies have demonstrated the emergence of chimera states in a variety of topologies and for different types of individual dynamics. In this paper, the interplay between initial conditions and non-local coupling is studied. We show that, based on an analytical argument incorporating the initial conditions and the range of non-local coupling, the occurrence of phase chimeras can be seen as caused by a phase lag in the coupling. Considering the dynamics of chimera states, our argument shows how “flipped” profiles of the mean phase velocities can be explained by a change of sign of the coupling phase. By this, one can either choose a concave (“upside”) profile of the mean phase velocities or a “flipped” one. Extending our reasoning, we show that this argument intuitively explains the transition from a phase- to an amplitude-mediated chimera state as a result of increasing coupling strength.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept