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Ghosh R, Verma UK, Jalan S, Shrimali MD. First-order transition to oscillation death in coupled oscillators with higher-order interactions. Phys Rev E 2023; 108:044207. [PMID: 37978677 DOI: 10.1103/physreve.108.044207] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 09/11/2023] [Indexed: 11/19/2023]
Abstract
We investigate the dynamical evolution of Stuart-Landau oscillators globally coupled through conjugate or dissimilar variables on simplicial complexes. We report a first-order explosive phase transition from an oscillatory state to oscillation death, with higher-order (2-simplex triadic) interactions, as opposed to the second-order transition with only pairwise (1-simplex) interactions. Moreover, the system displays four distinct homogeneous steady states in the presence of triadic interactions, in contrast to the two homogeneous steady states observed with dyadic interactions. We calculate the backward transition point analytically, confirming the numerical results and providing the origin of the dynamical states in the transition region. The results are robust against the application of noise. The study will be useful in understanding complex systems, such as ecological and epidemiological, having higher-order interactions and coupling through conjugate variables.
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Affiliation(s)
- Richita Ghosh
- Department of Physics, Central University of Rajasthan, Rajasthan, Ajmer-305 817, India
| | - Umesh Kumar Verma
- Complex Systems Laboratory, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453 552, India
| | - Sarika Jalan
- Complex Systems Laboratory, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453 552, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, Rajasthan, Ajmer-305 817, India
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Sathiyadevi K, Chandrasekar VK, Lakshmanan M. Emerging chimera states under nonidentical counter-rotating oscillators. Phys Rev E 2022; 105:034211. [PMID: 35428132 DOI: 10.1103/physreve.105.034211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Accepted: 03/04/2022] [Indexed: 06/14/2023]
Abstract
Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting corotating and counter-rotating systems. To illustrate the impact of counter-rotating frequencies, we consider a network of nonidentical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state in the oscillatory regime. Following this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity (P) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through a chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P symmetry, whereas the chimera state preserves the P symmetry only partially. To demonstrate the occurrence of such partial symmetry-breaking (chimera) state, we use basin stability analysis and discover that partial symmetry breaking exists as a result of the coexistence of symmetry-preserving and symmetry-breaking behavior in the initial state space. Further, a measure of the strength of P symmetry is established to quantify the P symmetry in the observed dynamical states. Subsequently, the dynamical transitions are investigated in the parametric spaces. Finally, by increasing the network size, the robustness of the chimera state is also inspected, and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related reduced phase. model as well as in other coupled models such as the globally coupled van der Pol and Rössler oscillators.
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Affiliation(s)
- K Sathiyadevi
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India
| | - V K Chandrasekar
- Department of Physics, Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, 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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Wein S, Deco G, Tomé AM, Goldhacker M, Malloni WM, Greenlee MW, Lang EW. Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:5573740. [PMID: 34135951 PMCID: PMC8177997 DOI: 10.1155/2021/5573740] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 05/06/2021] [Indexed: 12/12/2022]
Abstract
This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.
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Affiliation(s)
- Simon Wein
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Gustavo Deco
- Center for Brain and Cognition, Department of Technology and Information, University Pompeu Fabra, Carrer Tanger, 122-140, Barcelona 08018, Spain
- Institució Catalana de la Recerca i Estudis Avançats, University Barcelona, Passeig Lluís Companys 23, Barcelona 08010, Spain
| | - Ana Maria Tomé
- IEETA/DETI, University de Aveiro, Aveiro 3810-193, Portugal
| | - Markus Goldhacker
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Wilhelm M. Malloni
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Mark W. Greenlee
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Elmar W. Lang
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
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Chimera states in hybrid coupled neuron populations. Neural Netw 2020; 126:108-117. [DOI: 10.1016/j.neunet.2020.03.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 02/03/2020] [Accepted: 03/02/2020] [Indexed: 01/01/2023]
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Sathiyadevi K, Gowthaman I, Senthilkumar DV, Chandrasekar VK. Aging transition in the absence of inactive oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:123117. [PMID: 31893654 DOI: 10.1063/1.5121565] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 12/02/2019] [Indexed: 06/10/2023]
Abstract
The role of counter-rotating oscillators in an ensemble of coexisting co- and counter-rotating oscillators is examined by increasing the proportion of the latter. The phenomenon of aging transition was identified at a critical value of the ratio of the counter-rotating oscillators, which was otherwise realized only by increasing the number of inactive oscillators to a large extent. The effect of the mean-field feedback strength in the symmetry preserving coupling is also explored. The parameter space of aging transition was increased abruptly even for a feeble decrease in the feedback strength, and, subsequently, aging transition was observed at a critical value of the feedback strength surprisingly without any counter-rotating oscillators. Further, the study was extended to symmetry breaking coupling using conjugate variables, and it was observed that the symmetry breaking coupling can facilitate the onset of aging transition even in the absence of counter-rotating oscillators and for the unit value of the feedback strength. In general, the parameter space of aging transition was found to increase by increasing the frequency of oscillators and by increasing the proportion of the counter-rotating oscillators in both symmetry preserving and symmetry breaking couplings. Further, the transition from oscillatory to aging occurs via a Hopf bifurcation, while the transition from aging to oscillation death state emerges via the pitchfork bifurcation. Analytical expressions for the critical ratio of the counter-rotating oscillators are deduced to find the stable boundaries of the aging transition.
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Affiliation(s)
- K Sathiyadevi
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, Tamil Nadu 613 401, India
| | - I Gowthaman
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, Tamil Nadu 613 401, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram, Kerala 695551, India
| | - V K Chandrasekar
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, Tamil Nadu 613 401, India
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Kim J, Moon JY, Lee U, Kim S, Ko TW. Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:011106. [PMID: 30709108 PMCID: PMC6910590 DOI: 10.1063/1.5083621] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Accepted: 01/03/2019] [Indexed: 05/03/2023]
Abstract
We study the effects of coupling strength inhomogeneity and coupling functions on locking behaviors of coupled identical oscillators, some of which are relatively weakly coupled to others while some are relatively strongly coupled. Through the stability analysis and numerical simulations, we show that several categories of fully locked or partially locked states can emerge and obtain the conditions for these categories. In this system with coupling strength inhomogeneity, locked and drifting subpopulations are determined by the coupling strength distribution and the shape of the coupling functions. Even the strongly coupled oscillators can drift while weakly coupled oscillators can be locked. The simulation results with Gaussian and power-law distributions for coupling strengths are compared and discussed.
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Affiliation(s)
- Junhyeok Kim
- Nonlinear and Complex Systems Laboratory, Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
| | - Joon-Young Moon
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, Maryland 21209, USA
| | - Uncheol Lee
- Center for Consciousness Science, Department of Anesthesiology, University of Michigan Medical School, Ann Arbor, Michigan 48109, USA
| | - Seunghwan Kim
- Nonlinear and Complex Systems Laboratory, Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
| | - Tae-Wook Ko
- National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea
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