1
|
Kongni SJ, Nguefoue V, Njougouo T, Louodop P, Ferreira FF, Tchitnga R, Cerdeira HA. Phase transitions on a multiplex of swarmalators. Phys Rev E 2023; 108:034303. [PMID: 37849080 DOI: 10.1103/physreve.108.034303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 08/01/2023] [Indexed: 10/19/2023]
Abstract
Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range r_{c} which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync π has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength σ_{r} is very small for a fixed r_{c} and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of r_{c}. For σ_{r}=0 and for sufficiently small values of r_{c}, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling σ_{a} and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as σ_{a} increases. These results are supported by simulations and animations added as supplemental materials.
Collapse
Affiliation(s)
- Steve J Kongni
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Venceslas Nguefoue
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Thierry Njougouo
- Faculty of Computer Science and naXys Institute, University of Namur, 5000 Namur, Belgium; Namur Institute for Complex Systems (naXys), University of Namur, Belgium; Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P. O. Box 63, Buea, Cameroon; and MoCLiS Research Group, Dschang, Cameroon
| | - Patrick Louodop
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon; ICTP South American Institute for Fundamental Research, São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil; and MoCLiS Research Group, Dschang, Cameroon
| | - Fernando Fagundes Ferreira
- Center for Interdisciplinary Research on Complex Systems, University of Sao Paulo, São Paulo 03828-000, Brazil; and Department of Physics-FFCLRP, University of São Paulo, Ribeirão Preto, SP 14040-901, Brazil
| | - Robert Tchitnga
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon
| | - Hilda A Cerdeira
- São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil and Epistemic, Gomez & Gomez Ltda. ME, 05305-031 São Paulo, Brazil
| |
Collapse
|
2
|
Goldmann M, Mirasso CR, Fischer I, Soriano MC. Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatiotemporal systems using scalable neural networks. Phys Rev E 2022; 106:044211. [PMID: 36397530 DOI: 10.1103/physreve.106.044211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatiotemporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and by exploiting symmetry properties infers entire bifurcation diagrams.
Collapse
Affiliation(s)
- Mirko Goldmann
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears E-07122, Palma de Mallorca, Spain
| | - Claudio R Mirasso
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears E-07122, Palma de Mallorca, Spain
| | - Ingo Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears E-07122, Palma de Mallorca, Spain
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears E-07122, Palma de Mallorca, Spain
| |
Collapse
|
3
|
Kyrychko YN, Schwartz IB. Enhancing noise-induced switching times in systems with distributed delays. CHAOS (WOODBURY, N.Y.) 2018; 28:063106. [PMID: 29960399 DOI: 10.1063/1.5034106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions represent the most probable, or optimal, path, which maximizes the probability of escape. Explicit analytical results for the switching rates for small mean time delays are obtained for the uniform and bi-modal (or two-peak) distributions. They suggest that increasing the width of the distribution leads to an increase in the switching times even for longer values of mean time delays for both examples of the distribution kernel, and the increase is higher in the case of the two-peak distribution. Analytical predictions are compared to the direct numerical simulations and show excellent agreement between theory and numerical experiment.
Collapse
Affiliation(s)
- Y N Kyrychko
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
| | - I B Schwartz
- US Naval Research Laboratory, Code 6792, Nonlinear System Dynamics Section, Plasma Physics Division, Washington, DC 20375, USA
| |
Collapse
|
4
|
Erneux T, Javaloyes J, Wolfrum M, Yanchuk S. Introduction to Focus Issue: Time-delay dynamics. CHAOS (WOODBURY, N.Y.) 2017; 27:114201. [PMID: 29195312 DOI: 10.1063/1.5011354] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The field of dynamical systems with time delay is an active research area that connects practically all scientific disciplines including mathematics, physics, engineering, biology, neuroscience, physiology, economics, and many others. This Focus Issue brings together contributions from both experimental and theoretical groups and emphasizes a large variety of applications. In particular, lasers and optoelectronic oscillators subject to time-delayed feedbacks have been explored by several authors for their specific dynamical output, but also because they are ideal test-beds for experimental studies of delay induced phenomena. Topics include the control of cavity solitons, as light spots in spatially extended systems, new devices for chaos communication or random number generation, higher order locking phenomena between delay and laser oscillation period, and systematic bifurcation studies of mode-locked laser systems. Moreover, two original theoretical approaches are explored for the so-called Low Frequency Fluctuations, a particular chaotical regime in laser output which has attracted a lot of interest for more than 30 years. Current hot problems such as the synchronization properties of networks of delay-coupled units, novel stabilization techniques, and the large delay limit of a delay differential equation are also addressed in this special issue. In addition, analytical and numerical tools for bifurcation problems with or without noise and two reviews on concrete questions are proposed. The first review deals with the rich dynamics of simple delay climate models for El Nino Southern Oscillations, and the second review concentrates on neuromorphic photonic circuits where optical elements are used to emulate spiking neurons. Finally, two interesting biological problems are considered in this Focus Issue, namely, multi-strain epidemic models and the interaction of glucose and insulin for more effective treatment.
Collapse
Affiliation(s)
- Thomas Erneux
- Universite Libre de Bruxelles, 1050 Bruxelles, Belgium
| | - Julien Javaloyes
- Departament de Fisica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
| | | | - Serhiy Yanchuk
- Institute of Mathematics, Technical University of Berlin, Berlin, Germany
| |
Collapse
|