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Liang X, Liu C, Zhang X. Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators. Phys Rev E 2020; 101:022205. [PMID: 32168569 DOI: 10.1103/physreve.101.022205] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We investigate a system of globally coupled bistable oscillators subjected to a common weak signal, where the couplings are oscillator dependent with random signs: positive or negative. We find that neither purely positive nor purely negative couplings are optimal for signal amplification of the system; a mixture of both positive and negative couplings is more beneficial for the signal amplification. Our numerical results further show that different from the fully synchronous state caused by purely positive couplings or asynchronous state caused by purely negative couplings, the mixed positive and negative couplings can generate a clustering synchronous state, which allows the system to generate a resonancelike response to the weak signal, and thus, amplifies the signal. We finally propose a reduced model to analyze the mechanism underlying this resonancelike behavior, and find a complementary effect of these two types of couplings in signal amplification.
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Affiliation(s)
- Xiaoming Liang
- School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
| | - Cong Liu
- School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
| | - Xiyun Zhang
- Department of Physics, Jinan University, Guangzhou, Guangdong 510632, China
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2
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Qiu T, Boccaletti S, Liu Z, Guan S. Characterizing nonstationary coherent states in globally coupled conformist and contrarian oscillators. Phys Rev E 2019; 100:052310. [PMID: 31870024 DOI: 10.1103/physreve.100.052310] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2019] [Indexed: 11/07/2022]
Abstract
For decades, the description and characterization of nonstationary coherent states in coupled oscillators have not been available. We here consider the Kuramoto model consisting of conformist and contrarian oscillators. In the model, contrarians are chosen from a bimodal Lorentzian frequency distribution and flipped into conformists at random. A complete and systematic analytical treatment of the model is provided based on the Ott-Antonsen ansatz. In particular, we predict and analyze not only the stability of all stationary states (such as the incoherent, the π, and the traveling-wave states), but also that of the two nonstationary states: the Bellerophon and the oscillating-π state. The theoretical predictions are fully supported by extensive numerical simulations.
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Affiliation(s)
- Tian Qiu
- Department of Physics, East China Normal University, Shanghai 200241, China.,Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China
| | - S Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.,Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, China
| | - Zonghua Liu
- Department of Physics, East China Normal University, Shanghai 200241, China
| | - Shuguang Guan
- Department of Physics, East China Normal University, Shanghai 200241, China
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Saa A. Symmetries and synchronization in multilayer random networks. Phys Rev E 2018; 97:042304. [PMID: 29758722 DOI: 10.1103/physreve.97.042304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 06/08/2023]
Abstract
In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. We show, namely, that the presence of certain symmetries in the interlayer connection pattern tends to diminish the synchronization capability of the whole network or, in other words, asymmetries in the interlayer connections would enhance synchronization in such structured networks. Our results might help the understanding not only of the AISync mechanism itself but also its possible role in the determination of the interlayer connection pattern of multilayer and other structured networks with optimal synchronization properties.
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Affiliation(s)
- Alberto Saa
- Department of Applied Mathematics, University of Campinas, 13083-859 Campinas, SP, Brazil
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Qiu T, Zhang Y, Liu J, Bi H, Boccaletti S, Liu Z, Guan S. Landau damping effects in the synchronization of conformist and contrarian oscillators. Sci Rep 2015; 5:18235. [PMID: 26657060 PMCID: PMC4677401 DOI: 10.1038/srep18235] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2015] [Accepted: 11/13/2015] [Indexed: 11/30/2022] Open
Abstract
Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the incoherent state. We here show that such an effect is far more generic, as soon as phase oscillators couple to their mean field according to their natural frequencies, being then grouped into two distinct populations of conformists and contrarians. We report the analytical solution of this latter situation, which allows determining the critical coupling strength and the stability of the incoherent state, together with extensive numerical simulations that fully support all theoretical predictions. The relevance of our results is discussed in relationship to collective phenomena occurring in social and economical systems.
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Affiliation(s)
- Tian Qiu
- Department of Physics, East China Normal University, Shanghai, 200241, China
| | - Yue Zhang
- Department of Physics, East China Normal University, Shanghai, 200241, China
| | - Jie Liu
- Department of Physics, East China Normal University, Shanghai, 200241, China
| | - Hongjie Bi
- Department of Physics, East China Normal University, Shanghai, 200241, China
| | - S Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.,The Embassy of Italy in Tel Aviv, 25 Hamered street, 68125 Tel Aviv, Israel
| | - Zonghua Liu
- Department of Physics, East China Normal University, Shanghai, 200241, China.,State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Shuguang Guan
- Department of Physics, East China Normal University, Shanghai, 200241, China.,State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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Pinto RS, Saa A. Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062801. [PMID: 26764738 DOI: 10.1103/physreve.92.062801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2015] [Indexed: 05/16/2023]
Abstract
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function ω(T)Lω, where ω stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix. Many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition. A computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.
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Affiliation(s)
- Rafael S Pinto
- Instituto de Física "Gleb Wataghin," UNICAMP, 13083-859 Campinas, SP, Brazil
| | - Alberto Saa
- Departamento de Matemática Aplicada, UNICAMP, 13083-859 Campinas, SP, Brazil
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