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Koronovskii AA, Moskalenko OI, Selskii AO. Intermittent generalized synchronization and modified system approach: Discrete maps. Phys Rev E 2024; 109:064217. [PMID: 39020896 DOI: 10.1103/physreve.109.064217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 06/10/2024] [Indexed: 07/20/2024]
Abstract
The present work deals with the intermittent generalized synchronization regime observed near the boundary of generalized synchronization. The intermittent behavior is considered in the context of two observable phenomena, namely, (i) the birth of the asynchronous stages of motion from the complete synchronous state and (ii) the multistability in detection of the synchronous and asynchronous states. The mechanisms governing these phenomena are revealed and described in this paper with the help of the modified system approach for unidirectionally coupled model oscillators with discrete time.
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Anwar MS, Frolov N, Hramov AE, Ghosh D. Self-organized bistability on globally coupled higher-order networks. Phys Rev E 2024; 109:014225. [PMID: 38366474 DOI: 10.1103/physreve.109.014225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 01/04/2024] [Indexed: 02/18/2024]
Abstract
Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak-coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.
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Affiliation(s)
- Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Nikita Frolov
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, KU Leuven, Herestraat 49, 3000 Leuven, Belgium
| | - Alexander E Hramov
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo str., Kaliningrad 236016, Russia
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Frolov N, Hramov A. Self-organized bistability on scale-free networks. Phys Rev E 2022; 106:044301. [PMID: 36397487 DOI: 10.1103/physreve.106.044301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states under the self-tuning of a control parameter. Many of these systems have a network organization that should be taken into account to understand the underlying processes in detail. In the present paper, we theoretically explore an extension of the SOB concept on the scale-free network under coupling constraints. As provided by the numerical simulations and mean-field approximation in the thermodynamic limit, SOB on scale-free networks originates from facilitated criticality reflected on both macro- and mesoscopic network scales. We establish that the appearance of switches is rooted in spatial self-organization and temporal self-similarity of the network's critical dynamics and replicates extreme properties of epileptic seizure recurrences. Our results, thus, indicate that the proposed conceptual model is suitable to deepen the understanding of emergent collective behavior behind neurological diseases.
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Affiliation(s)
- Nikita Frolov
- Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad 236041, Russia and Institute of Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia
| | - Alexander Hramov
- Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad 236041, Russia and Institute of Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia
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Karpov OE, Grubov VV, Maksimenko VA, Kurkin SA, Smirnov NM, Utyashev NP, Andrikov DA, Shusharina NN, Hramov AE. Extreme value theory inspires explainable machine learning approach for seizure detection. Sci Rep 2022; 12:11474. [PMID: 35794223 PMCID: PMC9259747 DOI: 10.1038/s41598-022-15675-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 06/28/2022] [Indexed: 11/09/2022] Open
Abstract
Epilepsy is one of the brightest manifestations of extreme behavior in living systems. Extreme epileptic events are seizures, that arise suddenly and unpredictably. Usually, treatment strategies start by analyzing brain activity during the seizures revealing their type and onset mechanisms. This approach requires collecting data for a representative number of events which is only possible during the continuous EEG monitoring over several days. A big part of the further analysis is searching for seizures on these recordings. An experienced medical specialist spends hours checking the data of a single patient and needs assistance from the automative systems for seizure detection. Machine learning methods typically address this issue in a supervised fashion and exhibit a lack of generalization. The extreme value theory allows addressing this issue with the unsupervised machine learning methods of outlier detection. Here, we make the first step toward using this approach for the seizure detection. Based on our recent work, we specified the EEG features showing extreme behavior during seizures and loaded them to the one-class SVM, a popular outlier detection algorithm. Testing the proposed approach on 83 patients, we reported 77% sensitivity and 12% precision. In 60 patients, sensitivity was 100%. In the rest 23 subjects, we observed deviations from the extreme behavior. The one-class SVM used a single subject's data for training; therefore, it was stable against between-subject variability. Our results demonstrate an effective convergence between the extreme value theory, a physical concept, and the outlier detection algorithms, a machine learning concept, toward solving the meaningful task of medicine.
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Affiliation(s)
- Oleg E Karpov
- National Medical and Surgical Center named after N. I. Pirogov, Ministry of Healthcare of the Russian Federation, Moscow, Russia
| | - Vadim V Grubov
- Neuroscience and Cognitive Technology Laboratory, Innopolis University, Kazan, Russia.,Baltic Center for Artificial Intelligence and Neurotechnology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Vladimir A Maksimenko
- Neuroscience and Cognitive Technology Laboratory, Innopolis University, Kazan, Russia.,Baltic Center for Artificial Intelligence and Neurotechnology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Semen A Kurkin
- Neuroscience and Cognitive Technology Laboratory, Innopolis University, Kazan, Russia.,Baltic Center for Artificial Intelligence and Neurotechnology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Nikita M Smirnov
- Neuroscience and Cognitive Technology Laboratory, Innopolis University, Kazan, Russia
| | - Nikita P Utyashev
- National Medical and Surgical Center named after N. I. Pirogov, Ministry of Healthcare of the Russian Federation, Moscow, Russia
| | | | - Natalia N Shusharina
- Baltic Center for Artificial Intelligence and Neurotechnology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Alexander E Hramov
- Neuroscience and Cognitive Technology Laboratory, Innopolis University, Kazan, Russia. .,Baltic Center for Artificial Intelligence and Neurotechnology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia. .,Department of Theoretical Cybernetics, Saint Petersburg State University, St. Petersburg, Russia.
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Sulis W. The Continuum Between Temperament and Mental Illness as Dynamical Phases and Transitions. Front Psychiatry 2021; 11:614982. [PMID: 33536952 PMCID: PMC7848037 DOI: 10.3389/fpsyt.2020.614982] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 12/21/2020] [Indexed: 12/31/2022] Open
Abstract
The full range of biopsychosocial complexity is mind-boggling, spanning a vast range of spatiotemporal scales with complicated vertical, horizontal, and diagonal feedback interactions between contributing systems. It is unlikely that such complexity can be dealt with by a single model. One approach is to focus on a narrower range of phenomena which involve fewer systems but still cover the range of spatiotemporal scales. The suggestion is to focus on the relationship between temperament in healthy individuals and mental illness, which have been conjectured to lie along a continuum of neurobehavioral regulation involving neurochemical regulatory systems (e.g., monoamine and acetylcholine, opiate receptors, neuropeptides, oxytocin), and cortical regulatory systems (e.g., prefrontal, limbic). Temperament and mental illness are quintessentially dynamical phenomena, and need to be addressed in dynamical terms. A meteorological metaphor suggests similarities between temperament and chronic mental illness and climate, between individual behaviors and weather, and acute mental illness and frontal weather events. The transition from normative temperament to chronic mental illness is analogous to climate change. This leads to the conjecture that temperament and chronic mental illness describe distinct, high level, dynamical phases. This suggests approaching biopsychosocial complexity through the study of dynamical phases, their order and control parameters, and their phase transitions. Unlike transitions in physical systems, these biopsychosocial phase transitions involve information and semiotics. The application of complex adaptive dynamical systems theory has led to a host of markers including geometrical markers (periodicity, intermittency, recurrence, chaos) and analytical markers such as fluctuation spectroscopy, scaling, entropy, recurrence time. Clinically accessible biomarkers, in particular heart rate variability and activity markers have been suggested to distinguish these dynamical phases and to signal the presence of transitional states. A particular formal model of these dynamical phases will be presented based upon the process algebra, which has been used to model information flow in complex systems. In particular it describes the dual influences of energy and information on the dynamics of complex systems. The process algebra model is well-suited for dealing with the particular dynamical features of the continuum, which include transience, contextuality, and emergence. These dynamical phases will be described using the process algebra model and implications for clinical practice will be discussed.
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Affiliation(s)
- William Sulis
- Collective Intelligence Laboratory, Department of Psychiatry and Behavioural Neuroscience, McMaster University, Hamilton, ON, Canada
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Vera-Ávila VP, Sevilla-Escoboza JR, Leyva I. Complex networks exhibit intermittent synchronization. CHAOS (WOODBURY, N.Y.) 2020; 30:103119. [PMID: 33138450 DOI: 10.1063/5.0020419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 09/28/2020] [Indexed: 06/11/2023]
Abstract
The path toward the synchronization of an ensemble of dynamical units goes through a series of transitions determined by the dynamics and the structure of the connections network. In some systems on the verge of complete synchronization, intermittent synchronization, a time-dependent state where full synchronization alternates with non-synchronized periods, has been observed. This phenomenon has been recently considered to have functional relevance in neuronal ensembles and other networked biological systems close to criticality. We characterize the intermittent state as a function of the network topology to show that the different structures can encourage or inhibit the appearance of early signs of intermittency. In particular, we study the local intermittency and show how the nodes incorporate to intermittency in hierarchical order, which can provide information about the node topological role even when the structure is unknown.
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Affiliation(s)
- V P Vera-Ávila
- Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco 47460, Mexico
| | - J R Sevilla-Escoboza
- Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco 47460, Mexico
| | - I Leyva
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Madrid, Spain
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Choi D, Wishon MJ, Chang CY, Citrin DS, Locquet A. Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity. CHAOS (WOODBURY, N.Y.) 2018; 28:011102. [PMID: 29390638 DOI: 10.1063/1.5013332] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.
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Affiliation(s)
- Daeyoung Choi
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - Michael J Wishon
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - C Y Chang
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - D S Citrin
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - A Locquet
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
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