Delayed complex systems: an overview
2009; Royal Society; Volume: 368; Issue: 1911 Linguagem: Inglês
10.1098/rsta.2009.0243
ISSN1471-2962
AutoresWolfram Just, Axel Pelster, Michael Schanz, Eckehard Schöll,
Tópico(s)Complex Systems and Time Series Analysis
ResumoYou have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Just Wolfram, Pelster Axel, Schanz Michael and Schöll Eckehard 2010Delayed complex systems: an overviewPhil. Trans. R. Soc. A.368303–304http://doi.org/10.1098/rsta.2009.0243SectionYou have accessPrefaceDelayed complex systems: an overview Wolfram Just Wolfram Just School of Mathematical Sciences, Queen Mary University of London, London, UK [email protected] Google Scholar Find this author on PubMed Search for more papers by this author , Axel Pelster Axel Pelster Department of Physics, University of Duisburg-Essen, Duisburg, Germany Department of Physics and Astronomy, University of Potsdam, Potsdam, Germany Google Scholar Find this author on PubMed Search for more papers by this author , Michael Schanz Michael Schanz Institute of Parallel and Distributed Systems, University of Stuttgart, Stuttgart, Germany Google Scholar Find this author on PubMed Search for more papers by this author and Eckehard Schöll Eckehard Schöll Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany Google Scholar Find this author on PubMed Search for more papers by this author Wolfram Just Wolfram Just School of Mathematical Sciences, Queen Mary University of London, London, UK [email protected] Google Scholar Find this author on PubMed , Axel Pelster Axel Pelster Department of Physics, University of Duisburg-Essen, Duisburg, Germany Department of Physics and Astronomy, University of Potsdam, Potsdam, Germany Google Scholar Find this author on PubMed , Michael Schanz Michael Schanz Institute of Parallel and Distributed Systems, University of Stuttgart, Stuttgart, Germany Google Scholar Find this author on PubMed and Eckehard Schöll Eckehard Schöll Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany Google Scholar Find this author on PubMed Published:28 January 2010https://doi.org/10.1098/rsta.2009.0243There does not exist a generally accepted definition for the notion of complex systems in science, but it is a common belief that complex systems show features that cannot be explained by just looking at their constituents. Thus, a complex system normally involves interaction of subunits, and depending on the time scales, the propagation speed of information may become relevant for the dynamics. Therefore, it has been recognized nowadays that time delay may play a vital role in understanding complex behaviour.The new era of complexity science faces two challenges, namely dealing with the non-trivial topology of interacting subunits and the challenge caused by time delay, with the associated dynamics taking place in infinite-dimensional phase spaces. In the past, the subject of time-delay dynamics has been considered as a specialist topic so that only relatively few researchers were attracted. Within the last 15 years, research activities have considerably increased as many new applications have emerged in different areas, such as electronic engineering, controlling chaos, laser physics or neuroscience. Dynamics with time delay is going to play a vital role in new emerging fields of science and technology, for instance, because the speed of modern data processing does not allow finite propagation times of signals to be neglected any more. In addition, there are striking analogies between lasers and neural systems, in both of which delay effects are abundant.It is an intriguing feature of time delay that the phase space of any ordinary differential equation subjected to delay becomes infinite-dimensional. Hence, even simple equations of motion are able to produce extremely complex behaviour and bifurcation scenarios. Time delay has two complementary, counterintuitive and almost contradicting facets. On the one hand, delay is able to induce instabilities, bifurcations of periodic and more complicated orbits, multi-stability and chaotic motion. On the other hand, delay can suppress instabilities, stabilize unstable stationary or periodic states and may control complex chaotic dynamics.The recently held workshop on Delayed complex systems—from 5–9 October at the Max Planck Institute for the Physics of Complex Systems, Dresden, Germany—provided a forum for such topics. We took this opportunity to assemble a list of world-leading experts that now enables us to present an overview of the state of art in this field. The theme issue covers both applications and experiments, as well as mathematical foundations. The individual contributions summarize recent research results, but also address a broader context. Thus, the presentation is kept accessible for a large audience. The 12 articles cover all aspects of delay dynamics, ranging from control and stability, synchronization and numerical approximations, with applications in laser systems, neural science and engineering.The first contribution by Kestutis Pyragas and Tatjana Pyragienė addresses the issue of how to use time delay for the purpose of forecasting and to optimize the prediction horizon using dynamical-systems theory. The following five contributions are devoted to various aspects of synchronization and intermittency in time-delayed dynamical systems. The work by Bernold Fiedler et al. studies the synchronization of coupled oscillators by time-delayed feedback in a rigorous way. Thomas Murphy and collaborators give an overview of experimental strategies on synchronization of coupled optical elements. The contribution of Jordi Tiana Alsina et al. extends such an analysis to quantify the degree of synchronization in coupled semiconductor lasers using the concepts of symbolic dynamics. Synchronization of units with time delay can be efficiently used to establish a secure public key communication protocol, and the contribution by Wolfgang Kinzel and co-workers explains the fundamental ideas of such a concept. Finally, the article by Sebastian Brandstetter et al. provides a comprehensive overview of coupled FitzHugh–Nagumo systems, with a special emphasis on the effect of coloured noise and time-delayed feedback.The second half of the theme issue extends the scope to problems in digital engineering, the impact of imperfections and stochastic forces, as well as to biological systems. The contribution by Jason Boulet et al. addresses the problem of postural dynamics and identifies a critical time scale for the delay. The following two contributions study neural network models. The work by Gabor Orosz and co-workers describes how to use time-delayed feedback to regulate the behaviour of biological networks, and the article by Jérémie Lefebvre et al. presents a bifurcation analysis for a neural-network model of the sensory system. The work by Tamas Insperger and collaborators extends the focus of this issue to the fundamental aspects of control in engineering, in particular, the influence of digital delay on control performance. The penultimate contribution by Thomas Erneux and co-workers applies asymptotic methods to investigate front propagation in reaction–diffusion systems subjected to delay, and thus nicely supplements the previous studies on the FitzHugh–Nagumo model. We conclude this issue with a study on the emergence of chaos in digital circuits. Hugo L. D. de S. Cavalcante et al. discuss the mechanisms for generating chaotic motion in Boolean networks.We think this interdisciplinary theme issue may stimulate future developments and will encourage new interactions between different lines of research within this rapidly expanding vibrant field of delayed complex systems.FootnotesOne contribution of 13 to a Theme Issue 'Delayed complex systems'.© 2010 The Royal Society Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Jüngling T, Stemler T and Small M (2020) Laminar chaos in nonlinear electronic circuits with delay clock modulation, Physical Review E, 10.1103/PhysRevE.101.012215, 101:1 Cantisán J, Coccolo M, Seoane J and Sanjuán M (2020) Delay-Induced Resonance in the Time-Delayed Duffing Oscillator, International Journal of Bifurcation and Chaos, 10.1142/S0218127420300074, 30:03, (2030007), Online publication date: 15-Mar-2020. Müller-Bender D, Otto A and Radons G (2019) Resonant Doppler effect in systems with variable delay, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377:2153, Online publication date: 9-Sep-2019. Wernecke H, Sándor B and Gros C (2019) Chaos in time delay systems, an educational review, Physics Reports, 10.1016/j.physrep.2019.08.001, 824, (1-40), Online publication date: 1-Sep-2019. Müller D, Otto A and Radons G (2018) Laminar Chaos, Physical Review Letters, 10.1103/PhysRevLett.120.084102, 120:8 Rosinberg M, Tarjus G and Munakata T (2018) Influence of time delay on information exchanges between coupled linear stochastic systems, Physical Review E, 10.1103/PhysRevE.98.032130, 98:3 Müller D, Otto A and Radons G (2018) Dynamical Systems with Time-Varying Delay: Dissipative and More Dissipative Systems Complexity and Synergetics, 10.1007/978-3-319-64334-2_3, (27-37), . Li L and Xu J (2018) Bifurcation Analysis and Spatiotemporal Patterns in Unidirectionally Delay-Coupled Vibratory Gyroscopes, International Journal of Bifurcation and Chaos, 10.1142/S0218127418500293, 28:02, (1850029), Online publication date: 1-Feb-2018. Che Y and Cheng C (2018) Uncertainty quantification in stability analysis of chaotic systems with discrete delays, Chaos, Solitons & Fractals, 10.1016/j.chaos.2018.08.024, 116, (208-214), Online publication date: 1-Nov-2018. Otto A, Müller D and Radons G (2017) Universal Dichotomy for Dynamical Systems with Variable Delay, Physical Review Letters, 10.1103/PhysRevLett.118.044104, 118:4 Löber J (2017) Analytical Approximations for Optimal Trajectory Tracking Optimal Trajectory Tracking of Nonlinear Dynamical Systems, 10.1007/978-3-319-46574-6_4, (119-193), . Doedel E and L. C (2017) Periodic orbits and synchronous chaos in lasers unidirectionally coupled via saturable absorbers, The European Physical Journal Special Topics, 10.1140/epjst/e2016-60267-7, 226:3, (467-475), Online publication date: 1-Feb-2017. Teki H, Konishi K and Hara N (2017) Amplitude death in a pair of one-dimensional complex Ginzburg-Landau systems coupled by diffusive connections, Physical Review E, 10.1103/PhysRevE.95.062220, 95:6 Weicker L, Friart G and Erneux T (2017) Two distinct bifurcation routes for delayed optoelectronic oscillators, Physical Review E, 10.1103/PhysRevE.96.032206, 96:3 Erneux T, Javaloyes J, Wolfrum M and Yanchuk S (2017) Introduction to Focus Issue: Time-delay dynamics, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.5011354, 27:11, (114201), Online publication date: 1-Nov-2017. Watanabe T, Sugitani Y, Konishi K and Hara N (2017) Stability analysis of amplitude death in delay-coupled high-dimensional map networks and their design procedure, Physica D: Nonlinear Phenomena, 10.1016/j.physd.2016.07.011, 338, (26-33), Online publication date: 1-Jan-2017. Masoliver M, Malik N, Schöll E and Zakharova A (2017) Coherence resonance in a network of FitzHugh-Nagumo systems: Interplay of noise, time-delay, and topology, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.5003237, 27:10, (101102), Online publication date: 1-Oct-2017. Rosinberg M, Tarjus G and Munakata T (2017) Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations, Physical Review E, 10.1103/PhysRevE.95.022123, 95:2 Neofytou G, Kyrychko Y and Blyuss K (2017) Time-delayed model of RNA interference, Ecological Complexity, 10.1016/j.ecocom.2016.12.003, 30, (11-25), Online publication date: 1-Jun-2017. Hövel P, Lehnert J, Selivanov A, Fradkov A and Schöll E (2016) Adaptively Controlled Synchronization of Delay-Coupled Networks Control of Self-Organizing Nonlinear Systems, 10.1007/978-3-319-28028-8_3, (47-63), . Kantner M, Schöll E and Yanchuk S (2015) Delay-induced patterns in a two-dimensional lattice of coupled oscillators, Scientific Reports, 10.1038/srep08522, 5:1, Online publication date: 1-Jul-2015. Weicker L, Erneux T, Rosin D and Gauthier D (2015) Multirhythmicity in an optoelectronic oscillator with large delay, Physical Review E, 10.1103/PhysRevE.91.012910, 91:1 Kopylov W, Radonjić M, Brandes T, Balaž A and Pelster A (2015) Dissipative two-mode Tavis-Cummings model with time-delayed feedback control, Physical Review A, 10.1103/PhysRevA.92.063832, 92:6 Amil P, Cabeza C, Masoller C and Martí A (2015) Organization and identification of solutions in the time-delayed Mackey-Glass model, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.4918593, 25:4, (043112), Online publication date: 1-Apr-2015. Punetha N, Ujjwal S, Atay F and Ramaswamy R (2015) Delay-induced remote synchronization in bipartite networks of phase oscillators, Physical Review E, 10.1103/PhysRevE.91.022922, 91:2 Rosin D (2015) Introduction Dynamics of Complex Autonomous Boolean Networks, 10.1007/978-3-319-13578-6_1, (1-12), . Choe C, Kim R, Jang H, Hövel P and Schöll E (2014) Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays, International Journal of Dynamics and Control, 10.1007/s40435-013-0049-2, 2:1, (2-25), Online publication date: 1-Mar-2014. Geffert P, Zakharova A, Vüllings A, Just W and Schöll E (2014) Modulating coherence resonance in non-excitable systems by time-delayed feedback, The European Physical Journal B, 10.1140/epjb/e2014-50541-2, 87:12, Online publication date: 1-Dec-2014. Kyrychko Y, Blyuss K and Schöll E (2013) Amplitude and phase dynamics in oscillators with distributed-delay coupling, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371:1999, Online publication date: 28-Sep-2013. D'Odorico P, Ridolfi L and Laio F (2013) Precursors of state transitions in stochastic systems with delay, Theoretical Ecology, 10.1007/s12080-013-0188-2, 6:3, (265-270), Online publication date: 1-Aug-2013. D'Huys O, Zeeb S, Jüngling T, Heiligenthal S, Yanchuk S and Kinzel W (2013) Synchronisation and scaling properties of chaotic networks with multiple delays, EPL (Europhysics Letters), 10.1209/0295-5075/103/10013, 103:1, (10013), Online publication date: 1-Jul-2013. Heiligenthal S, Jüngling T, D'Huys O, Arroyo-Almanza D, Soriano M, Fischer I, Kanter I and Kinzel W (2013) Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings, Physical Review E, 10.1103/PhysRevE.88.012902, 88:1 Soriano M, García-Ojalvo J, Mirasso C and Fischer I (2013) Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers, Reviews of Modern Physics, 10.1103/RevModPhys.85.421, 85:1, (421-470) D'Odorico P, Laio F and Ridolfi L (2012) Noise-sustained fluctuations in stochastic dynamics with a delay, Physical Review E, 10.1103/PhysRevE.85.041106, 85:4 Yongli Song and Jian Xu Inphase and Antiphase Synchronization in a Delay-Coupled System With Applications to a Delay-Coupled FitzHugh–Nagumo System, IEEE Transactions on Neural Networks and Learning Systems, 10.1109/TNNLS.2012.2209459, 23:10, (1659-1670) Weicker L, Erneux T, D'Huys O, Danckaert J, Jacquot M, Chembo Y and Larger L (2012) Strongly asymmetric square waves in a time-delayed system, Physical Review E, 10.1103/PhysRevE.86.055201, 86:5 D'Huys O, Fischer I, Danckaert J and Vicente R (2012) Spectral and correlation properties of rings of delay-coupled elements: Comparing linear and nonlinear systems, Physical Review E, 10.1103/PhysRevE.85.056209, 85:5 Weicker L, Erneux T, Jacquot M, Chembo Y and Larger L (2012) Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator, Physical Review E, 10.1103/PhysRevE.85.026206, 85:2 Guill C, Reichardt B, Drossel B and Just W (2011) Coexisting patterns of population oscillations: The degenerate Neimark-Sacker bifurcation as a generic mechanism, Physical Review E, 10.1103/PhysRevE.83.021910, 83:2 Hicke K, D'Huys O, Flunkert V, Schöll E, Danckaert J and Fischer I (2011) Mismatch and synchronization: Influence of asymmetries in systems of two delay-coupled lasers, Physical Review E, 10.1103/PhysRevE.83.056211, 83:5 Flunkert V and Schöll E (2011) Towards easier realization of time-delayed feedback control of odd-number orbits, Physical Review E, 10.1103/PhysRevE.84.016214, 84:1 Kyrychko Y, Blyuss K and Schöll E (2011) Amplitude death in systems of coupled oscillators with distributed-delay coupling, The European Physical Journal B, 10.1140/epjb/e2011-20677-8, 84:2, (307-315), Online publication date: 1-Nov-2011. Heiligenthal S, Dahms T, Yanchuk S, Jüngling T, Flunkert V, Kanter I, Schöll E and Kinzel W (2011) Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings, Physical Review Letters, 10.1103/PhysRevLett.107.234102, 107:23 von Loewenich C, Benner H and Just W (2010) Experimental verification of Pyragas-Schöll-Fiedler control, Physical Review E, 10.1103/PhysRevE.82.036204, 82:3 D'Huys O, Vicente R, Danckaert J and Fischer I (2010) Amplitude and phase effects on the synchronization of delay-coupled oscillators, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.3518363, 20:4, (043127), Online publication date: 1-Dec-2010. Kouvaris N, Schimansky-Geier L and Schöll E (2011) Control of coherence in excitable systems by the interplay of noise and time-delay, The European Physical Journal Special Topics, 10.1140/epjst/e2010-01340-x, 191:1, (29-51), Online publication date: 1-Dec-2010. This Issue28 January 2010Volume 368Issue 1911Theme Issue 'Delayed complex systems' compiled and edited by Wolfram Just, Axel Pelster, Michael Schanz and Eckehard Schöll Article InformationDOI:https://doi.org/10.1098/rsta.2009.0243Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online28/01/2010Published in print28/01/2010 License:© 2010 The Royal Society Citations and impact PDF Download Subjectscomplexity
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