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Qian Y, Han J, Yang R, Chen W, Lei Z, Zheng Z. Emergence of chimeralike oscillation modes in excitable complex networks with preferentially cutting-rewiring operation. CHAOS (WOODBURY, N.Y.) 2024; 34:063143. [PMID: 38934725 DOI: 10.1063/5.0167251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 06/05/2024] [Indexed: 06/28/2024]
Abstract
In this paper, the preferentially cutting-rewiring operation (PCRO) consisting of the cutting procedure and the rewiring procedure is proposed and is applied on an excitable Erdös-Rényi random network (EERRN), by which the structure of the initially homogeneous network changes dramatically, and lots of common leaves (CLs) are formed between the two hubs. Subsequently, besides the single-mode oscillations that can be usually observed in homogeneous excitable systems, a new kind of multi-mode oscillations composed of synchronous and asynchronous parts can self-organize to emerge, which are similar to the coherent and incoherent clusters in traditional chimera states and are consequently named as the chimeralike oscillation modes (CLOMs). Importantly, by utilizing the dominant phase-advanced driving method, both the mechanisms for the formation and the emergence of CLOMs in EERRNs with PCRO are well explained, among which the CL is exposed to play a key role in forming the CLOMs. Furthermore, the PCRO-induced CLOM phenomena can also be observed in other paradigmatic network models or with other paradigmatic excitable dynamics, which definitely confirms that the PCRO is an universal method in inducing the CLOMs in excitable complex networks. Our contributions may shed lights on a new perspective of the emergence of CLOMs in complex systems and would have great impacts in related fields.
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Affiliation(s)
- Yu Qian
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Jing Han
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Runru Yang
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Wentao Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China
| | - Zhao Lei
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Zhigang Zheng
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China
- College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
- School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
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2
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Kar R, Yadav A, Chandrasekar VK, Senthilkumar DV. Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators. CHAOS (WOODBURY, N.Y.) 2024; 34:023110. [PMID: 38363957 DOI: 10.1063/5.0181279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 01/23/2024] [Indexed: 02/18/2024]
Abstract
We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams. The higher-order interaction facilitates the onset of the bifurcation transitions at a much lower disparity between the inter- and intra-population coupling strengths. Furthermore, the higher-order interaction facilitates the spread of breathing chimera in a large region of the parameter space while suppressing the spread of the stable chimera. A low degree of heterogeneity among the phase-lag parameters promotes the spread of both stable chimera and breathing chimera to a large region of the parameter space for a large fraction of the higher-order coupling. In contrast, a large degree of heterogeneity is found to decrease the spread of both chimera states for a large fraction of the higher-order coupling. A global synchronized state is observed above a critical value of heterogeneity among the phase-lag parameters. We have deduced the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen Ansatz. We have also deduced the analytical saddle-node and Hopf bifurcation curves from the evolution equations for the macroscopic order parameters and found them to match with the bifurcation curves obtained using the software XPPAUT and with the simulation results.
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Affiliation(s)
- Rumi Kar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
| | - Akash Yadav
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
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Zheng Z, Xu C, Fan J, Liu M, Chen X. Order parameter dynamics in complex systems: From models to data. CHAOS (WOODBURY, N.Y.) 2024; 34:022101. [PMID: 38341762 DOI: 10.1063/5.0180340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 12/14/2023] [Indexed: 02/13/2024]
Abstract
Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements in complex systems may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity in describing the transition to collective states, may emerge spontaneously from large numbers of degrees of freedom through competitions. In this minireview, we extensively discussed the collective dynamics of complex systems from the viewpoint of order-parameter dynamics. A synergetic theory is adopted as the foundation of order-parameter dynamics, and it focuses on the self-organization and collective behaviors of complex systems. At the onset of macroscopic transitions, slow modes are distinguished from fast modes and act as order parameters, whose evolution can be established in terms of the slaving principle. We explore order-parameter dynamics in both model-based and data-based scenarios. For situations where microscopic dynamics modeling is available, as prototype examples, synchronization of coupled phase oscillators, chimera states, and neuron network dynamics are analytically studied, and the order-parameter dynamics is constructed in terms of reduction procedures such as the Ott-Antonsen ansatz, the Lorentz ansatz, and so on. For complicated systems highly challenging to be well modeled, we proposed the eigen-microstate approach (EMP) to reconstruct the macroscopic order-parameter dynamics, where the spatiotemporal evolution brought by big data can be well decomposed into eigenmodes, and the macroscopic collective behavior can be traced by Bose-Einstein condensation-like transitions and the emergence of dominant eigenmodes. The EMP is successfully applied to some typical examples, such as phase transitions in the Ising model, climate dynamics in earth systems, fluctuation patterns in stock markets, and collective motion in living systems.
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Affiliation(s)
- Zhigang Zheng
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
| | - Can Xu
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
| | - Jingfang Fan
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
| | - Maoxin Liu
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
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Gu S, Fang Q, Zhou P, Li N. Chimera states in a large laterally coupled laser array with four different waveguide structures. CHAOS (WOODBURY, N.Y.) 2023; 33:073152. [PMID: 37499249 DOI: 10.1063/5.0151330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 07/03/2023] [Indexed: 07/29/2023]
Abstract
Chimera states are rich and fascinating phenomena existing in many networks, where the identical oscillators self-organize into spatially separated coexisting domains of coherent and incoherent oscillations. Here, we report these states in the large laterally coupled laser array with four different waveguiding structures, with which a variety of chimera patterns can be revealed. We present the bifurcation diagrams giving birth to them and find that the chimeras exist in the boundary of the steady state and multi-period oscillation solutions, which applies to all the prevalent waveguiding structures considered. We also find that the waveguiding structures play an important role in the chimera states, e.g., the array composed of the index antiguiding with gain-guiding has a wider chimera region compared to other waveguides considered. Additionally, the effects of the crucial parameters including the laser separation ratio, pump rate, frequency detuning, and linewidth enhancement factor on the observed phenomena are discussed. Our analysis shows that the frequency detuning between lasers and the linewidth enhancement factor affects the lifetime and pattern of chimeras. The results could guide the design of laser arrays or introduce more insight into a new understanding of the dynamical behaviors of networks.
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Affiliation(s)
- Shuangquan Gu
- School of Optoelectronic Science and Engineering and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
- Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
| | - Qi Fang
- School of Optoelectronic Science and Engineering and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
- Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
| | - Pei Zhou
- School of Optoelectronic Science and Engineering and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
- Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
| | - Nianqiang Li
- School of Optoelectronic Science and Engineering and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
- Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
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Bi H, Fukai T. Amplitude-mediated chimera states in nonlocally coupled Stuart-Landau oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:083125. [PMID: 36049944 DOI: 10.1063/5.0096284] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
Chimera states achieve the coexistence of coherent and incoherent subgroups through symmetry breaking and emerge in physical, chemical, and biological systems. We show the presence of amplitude-mediated multicluster chimera states in nonlocally coupled Stuart-Landau oscillators. We clarify the prerequisites for having different types of chimera states by analytically and numerically studying how phase transitions occur between these states. Our results demonstrate how the oscillation amplitudes interact with the phase degrees of freedom in chimera states and significantly advance our understanding of the generation mechanisms of such states in coupled oscillator systems.
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Affiliation(s)
- Hongjie Bi
- Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan
| | - Tomoki Fukai
- Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan
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Kachhara S, Ambika G. Frequency chimera state induced by differing dynamical timescales. Phys Rev E 2021; 104:064214. [PMID: 35030851 DOI: 10.1103/physreve.104.064214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Accepted: 12/04/2021] [Indexed: 06/14/2023]
Abstract
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is generated by the local coupling among nonlinear oscillators evolving under differing dynamical timescales starting from random initial conditions. We show how they self-organize to structured patterns with spatial domains of coherence that are in frequency synchronization, coexisting with domains that are incoherent in frequencies. Our study has relevance in understanding such patterns observed in real-world systems like neuronal systems, power grids, social and ecological networks, where differing dynamical timescales is natural and realistic among the interacting systems.
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Affiliation(s)
- Sneha Kachhara
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
| | - G Ambika
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
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Mehrabbeik M, Parastesh F, Ramadoss J, Rajagopal K, Namazi H, Jafari S. Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:9394-9409. [PMID: 34814351 DOI: 10.3934/mbe.2021462] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.
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Affiliation(s)
- Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
| | - Janarthanan Ramadoss
- Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Hamidreza Namazi
- School of Engineering, Monash University, Selangor, Malaysia
- College of Engineering and Science, Victoria University, Melbourne, Australia
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
- Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
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Kundu S, Muruganandam P, Ghosh D, Lakshmanan M. Amplitude-mediated spiral chimera pattern in a nonlinear reaction-diffusion system. Phys Rev E 2021; 103:062209. [PMID: 34271612 DOI: 10.1103/physreve.103.062209] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 05/21/2021] [Indexed: 11/07/2022]
Abstract
Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study that is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in the presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely, spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude-mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady-state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.
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Affiliation(s)
- Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | | | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli-620024, India
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Wang J, Zou W. Collective behaviors of mean-field coupled Stuart-Landau limit-cycle oscillators under additional repulsive links. CHAOS (WOODBURY, N.Y.) 2021; 31:073107. [PMID: 34340324 DOI: 10.1063/5.0050698] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 06/15/2021] [Indexed: 06/13/2023]
Abstract
We study the collective behaviors of a large population of Stuart-Landau limit-cycle oscillators that coupled diffusively and equally with all of the others via the conjugate of the mean field, where the underlying interaction is shown to break the rotational symmetry of the coupled system. In the model, an ensemble of Stuart-Landau oscillators are in fact diffusively coupled via the mean field in the real parts, whereas additional repulsive links are present in the imaginary parts. All the oscillators are linked via the similar state variables, which distinctly differs from the conjugate coupling through dissimilar variables in the previous studies. We show that depending on the strength of coupling and the distribution of natural frequencies, the coupled system exhibits three qualitatively different types of collective stationary behaviors: amplitude death (AD), oscillation death (OD), and incoherent state. Our goal is to analytically characterize the onset of the above three typical macrostates by performing the rigorous linear stability analyses of the corresponding mean-field coupled system. We prove that AD is able to occur in the coupled system with identical frequencies, where the stable coupling interval of AD is found to be independent on the system's size N. When the natural frequencies are distributed according to a general density function, we obtain the analytic equations that govern the exact stability boundaries of AD, OD, and the incoherence for a coupled system in the thermodynamic limit N→∞. All the theoretical predictions are well confirmed via numerical simulations of the coupled system with a specific Lorentzian frequency distribution.
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Affiliation(s)
- Jianwei Wang
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
| | - Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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