Nonlocally Coupled Research Articles

Clustered chimera states in systems of type-I excitability

The chimera state is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras have been found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative of neural excitability type I. We obtain chimera states with multiple coherent regions (clustered chimeras/multi-chimeras) depending on the distance from the excitability threshold, the range of nonlocal coupling and the coupling strength. A detailed stability diagram for these chimera states and other interesting coexisting patterns (like traveling waves) is presented.

Single photon transport properties in coupled cavity arrays nonlocally coupled to a two-level atom in the presence of dissipation

We discuss the effects of dissipation on the behavior of single photon transport in a system of coupled cavity arrays, with the two nearest cavities nonlocally coupled to a two-level atom. The single photon transmission amplitude is solved exactly by employing the quasi-boson picture. We investigate two different situations of local and nonlocal couplings, respectively. Comparing the dissipative case with the nondissipative one reveals that the dissipation of the system increases the middle dip and lowers the peak of the single photon transmission amplitudes, broadening the line width of the transport spectrum. It should be noted that the influence of the cavity dissipation to the single photon transport spectrum is asymmetric. By comparing the nonlocal coupling with the local one, one can find that the enhancement of the middle dip of single photon transmission amplitudes is mostly caused by the atom dissipation and that the reduced peak is mainly caused by the cavity dissipation, no matter whether it is a nonlocal or local coupling case. Whereas in the nonlocal coupling case, when the coupling strength gets stronger, the cavity dissipation has a greater effect on the single photon transport spectrum and the atom dissipation affection becomes weak, so it can be ignored.

A SYSTEMATIC STUDY OF NONLOCALLY COUPLED OSCILLATORS AND CHIMERA STATES

Oscillators under nonlocal couplings are systematically studied. We propose functions of inverse power as mathematical realization for nonlocal couplings among oscillators in a system. Power β in a function is taken as an important parameter in our study. Since its value determines a measure of "localization" while oscillators are nonlocally coupled it is then called the "nonlocal parameter". Together with the "phase lag parameter" α, which is vital for the existence of chimera states, we are able to demonstrate a valuable phase portrait in the β-α space. System dynamics is discussed in this phase diagram analogous to phase transitions in thermodynamics.

Multi-chimera states in FitzHugh-Nagumo oscillators

Chimera states are spatio-temporal patterns of synchrony and disorder observed in homogeneous oscillatory media with nonlocal coupling. They are characterized by coexistence of distinct spatial regions with regular synchronized and irregular incoherent motion. Initially discovered for phase oscillators, chimera states have been also found in systems of nonlocally coupled discrete maps [1], time-continuous chaotic systems [2] and have been recently realized in experiments [3]. We demonstrate the existence of chimera states for neural oscillators [4]. In detail, we investigate the cooperative dynamics of nonlocally coupled neural populations modeled by FitzHugh-Nagumo systems, where each individual system displays oscillatory local dynamics described by a fast activator and slow inhibitor variable. Applying a phase-reduction technique we show that off-diagonal nonlocal coupling is a crucial factor for the appearance of chimera states. In the considered configuration, this off-diagonal coupling is realized by a rotational coupling matrix that mixes input of the activator and inhibitor and that is conveniently described by the coupling phase as a single control parameter. We analyze the stability of chimera states in the parameter space of the system and discuss mechanisms of transitions between different chimera types. Surprisingly, we find that for increasing coupling strength classical chimera states undergo transitions from one to multiple domains of incoherence. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multi-chimeras arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

When Nonlocal Coupling between Oscillators Becomes Stronger: Patched Synchrony or Multichimera States

Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multichimera states arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

Experimental observation of chimeras in coupled-map lattices

In systems of oscillators, phase-locking behaviour can, in theory, coexist with incoherent dynamics—invoking the fabled chimera state. Now, experimental realization of a coupled-map lattice reveals dynamical states displaying coexisting spatial domains of coherence and incoherence. Networks of nonlocally coupled phase oscillators1 can support chimera states in which identical oscillators evolve into distinct groups that exhibit coexisting synchronous and incoherent behaviours despite homogeneous coupling2,3,4,5,6. Similar nonlocal coupling topologies implemented in networks of chaotic iterated maps also yield dynamical states exhibiting coexisting spatial domains of coherence and incoherence7,8. In these discrete-time systems, the phase is not a continuous variable, so these states are generalized chimeras with respect to a broader notion of incoherence. Chimeras continue to be the subject of intense theoretical investigation, but have yet to be realized experimentally6,9,10,11,12,13,14,15,16. Here we show that these chimeras can be realized in experiments using a liquid-crystal spatial light modulator to achieve optical nonlinearity in a spatially extended iterated map system. We study the coherence–incoherence transition that gives rise to these chimera states through experiment, theory and simulation.

Effects of nonlocal coupling on the dynamics of neural systems

Event Abstract Back to Event Effects of nonlocal coupling on the dynamics of neural systems Philipp Hövel1, 2* and Iryna Omelchenko1, 2 1 Technische Universität Berlin, Physics, Germany 2 Bernstein Center for Computational Neuroscience Berlin, Germany Understanding the dynamics on networks is at the heart of modern nonlinear science and has a wide applicability to neuroscience. The interplay of network topology and local dynamics opens a variety of dynamical phenomena such as synchronization, clustering, waves, kinks, complex patterns, and chaos. Here we study the spatio-temporal dynamics of coupled neural oscillators with nonlocal interactions. In the considered configuration each element is coupled to its nearest neighbors within a finite range. Depending upon the control parameters chosen as coupling strength and coupling radius, we investigate the cooperative dynamics in a generic model for type-II excitability given by FitzHugh-Nagumo equations. The individual systems are considered to operate above a Hopf bifurcation, that is, they operate in the oscillatory regime. On the basis of previous results on nonlocally coupled discrete maps and chaotic systems, we demonstrate the universality of a transition from coherence to incoherence in such systems, giving rise to spatial chaos and so-called chimera states. The latter arise as hybrid spatial patterns in regular networks of identical oscillators and consist of parts with high spatial coherence and regions where spatial coherence is lost. We analyze the regions of stability of various types of solutions in the parameter space of coupling strength and coupling radius: completely synchronous oscillations, wave-like profiles, cluster states as well as partially incoherent states. Furthermore, we study the robustness of the observed patterns in the presence of inhomogeneities of the local elements that are introduced via different threshold parameters in the FitzHugh-Nagumo system. Acknowledgements Supported by the BMBF under the grant no. 01GQ1001B (Förderkennzeichen). Keywords: dynamics, incoherence, nonlocal coupling, oscillations, synchronization Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012. Presentation Type: Poster Topic: Abstracts Citation: Hövel P and Omelchenko I (2012). Effects of nonlocal coupling on the dynamics of neural systems. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00221 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 10 May 2012; Published Online: 12 Sep 2012. * Correspondence: Dr. Philipp Hövel, Technische Universität Berlin, Physics, Berlin, 10623, Germany, phoevel@physik.tu-berlin.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Philipp Hövel Iryna Omelchenko Google Philipp Hövel Iryna Omelchenko Google Scholar Philipp Hövel Iryna Omelchenko PubMed Philipp Hövel Iryna Omelchenko Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Nonlocal dilaton coupling to dark matter: Cosmic acceleration and pressure backreaction

A model of nonlocal dilaton interactions, motivated by string duality symmetries, is applied to a scenario of ``coupled quintessence'' in which the dilaton dark energy is nonlocally coupled to the dark-matter sources. It is shown that the nonlocal effects tend to generate a backreaction which---for strong enough coupling---can automatically compensate the acceleration due to the negative pressure of the dilaton potential, thus asymptotically restoring the standard (dust-dominated) decelerated regime. This result is illustrated by analytical computations and numerical examples.

Ballistic four-terminal Josephson junction: bistable states and magnetic flux transfer

The macroscopic quantum interference effects in the ballistic Josephson microstructures are investigated. The studied system comprises four bulk superconductors (terminals) which are weakly coupled through a mesoscopic rectangular normal metal layer (two-dimensional electron gas). We show that nonlocal electrodynamics of ballistic systems lead to specific current–phase relations for the mesoscopic multiterminal Josephson junction. The nonlocal coupling of supercurrents produces a “dragging” effect for phases of the superconducting order parameter in different terminals. The composite Josephson junction, based on this effect, exhibits the two-level system behaviour controlled by the external magnetic flux. The effect of magnetic flux transfer in a system of nonlocally coupled superconducting rings is also studied.

Dynamics of spatial structures in arrays of nonlocally coupled bistable units

We present the results of investigation of a dynamical system consisting of nonlocally coupled bistable units. The dynamics of spatial structures in an array with a gradually increasing coupling coefficient is studied. The formation of spatial structures in the case of strong nonlocal coupling between units is examined.