1. Aging transitions of multimodal oscillators in multilayer networksUroš Barać, Matjaž Perc, Marko Gosak, 2024, izvirni znanstveni članek Opis: When individual oscillators age and become inactive, the collective dynamics of coupled oscillators is often affected as well. Depending on the fraction of inactive oscillators or cascading failures that percolate from crucial information exchange points, the critical shift toward macroscopic inactivity in coupled oscillator networks is known as the aging transition. Here, we study this phenomenon in two overlayed square lattices that together constitute a multilayer network, whereby one layer is populated with slow Poincaré oscillators and the other with fast Rulkov neurons. Moreover, in this multimodal setup, the excitability of fast oscillators is influenced by the phase of slow oscillators that are gradually inactivated toward the aging transition in the fast layer. Through extensive numerical simulations, we find that the progressive inactivation of oscillators in the slow layer nontrivially affects the collective oscillatory activity and the aging transitions in the fast layer. Most counterintuitively, we show that it is possible for the intensity of oscillatory activity in the fast layer to progressively increase to up to 100%, even when up to 60% of units in the slow oscillatory layer are inactivated. We explain our results with a numerical analysis of collective behavior in individual layers, and we discuss their implications for biological systems.
Ključne besede: collective dynamics, coupled oscillators, dynamics of networks, network resilience, robustness, synchronization transition
Objavljeno v DKUM: 28.02.2025; Ogledov: 0; Prenosov: 425
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2. Minimal universal laser network model : synchronization, extreme events, and multistabilityMahtab Mehrabbeik, Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, Riccardo Meucci, 2024, izvirni znanstveni članek Opis: The synchronization of chaotic systems has garnered considerable attention across various fields, including neuroscience and physics. Particularly in these domains, synchronizing physical systems such as laser models is crucial for secure and rapid information transmission. Consequently, numerous studies investigate the synchronizability of different laser networks by establishing logical network frameworks. In this study, we employed a minimal universal laser (MUL) model designed to capture the essential dynamics of an actual laser model within just three dimensions. Within the network model of MUL systems, we introduced the linear diffusive function of neighboring nodes' fast variables into the feedback term of the lasers, with models arranged in a global network structure. Our examination of synchronization within the constructed MUL network utilized master stability functions and the time-averaged synchronization error index. The findings suggest that while the network fails to achieve complete synchrony, it exhibits various synchronization phenomena, including cluster synchronization, chimera states, extreme events, and multistability. These results shed light on the complex dynamics underlying the synchronization of chaotic systems in networked environments, offering insights relevant to numerous applications across diverse fields.
Ključne besede: minimal universal laser model, synchronization, extreme events
Objavljeno v DKUM: 16.12.2024; Ogledov: 0; Prenosov: 4
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3. Global synchronization in generalized multilayer higher-order networksPalash Kumar Pal, Md Sayeed Anwar, Matjaž Perc, Dibakar Ghosh, 2024, izvirni znanstveni članek Opis: Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited to specific models, such as the Kuramoto model, or have focused solely on higher-order interactions within individual layers. Here, we present a comprehensive framework for investigating synchronization, particularly global synchronization, in multilayer networks with higher-order interactions. Our framework considers interactions beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state, with a condition resembling the master stability function, contingent on the choice of coupling functions. Our theoretical findings are supported by simulations using Hindmarsh-Rose neuronal and Rössler oscillators. These simulations illustrate how synchronization is facilitated by higher-order interactions, both within and across layers, highlighting the advantages over scenarios involving interactions within single layers.
Ključne besede: synchronization, network, phase transition, statistical physics
Objavljeno v DKUM: 27.11.2024; Ogledov: 0; Prenosov: 2
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4. Collective dynamics of heterogeneously and nonlinearly coupled phase oscillatorsCan Xu, Xiaohuan Tang, Huaping Lü, Karin Alfaro-Bittner, Stefano Boccaletti, Matjaž Perc, Shuguang Guan, 2021, izvirni znanstveni članek Opis: Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a variant of the Kuramoto model, where the coupling between the phase oscillators is heterogeneous and nonlinear. In particular, the quenched disorder in the coupling strength and the intrinsic frequencies are correlated, and the coupling itself depends on the amplitude of the mean field of the system. We show that the interplay of these factors leads to a fascinatingly rich collective dynamics, including explosive synchronization transitions, hybrid transitions with hysteresis absence, abrupt irreversible desynchronization transitions, and tiered phase transitions with or without a vanishing onset. We develop an analytical treatment that enables us to determine the observed equilibrium states of the system, as well as to explore their asymptotic stability at various levels. Our research thus provides theoretical foundations for a number of self-organized phenomena that may be responsible for the emergence of collective rhythms in complex systems.
Ključne besede: coupled oscillators, synchronization, Kuramoto model, collective dynamics, phase transition
Objavljeno v DKUM: 22.10.2024; Ogledov: 0; Prenosov: 4
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5. Dynamics on higher-order networks: a reviewSoumen Majhi, Matjaž Perc, Dibakar Ghosh, 2022, pregledni znanstveni članek Opis: Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological and technological systems, higher-order networks have recently led to important new discoveries across many fields of research. Here, we review these works, focusing in particular on the novel aspects of the dynamics that emerges on higher-order networks. We cover a variety of dynamical processes that have thus far been studied, including different synchronization phenomena, contagion processes, the evolution of cooperation and consensus formation. We also outline open challenges and promising directions for future research.
Ključne besede: higher-order networks, synchronization, cooperation, dynamics
Objavljeno v DKUM: 17.09.2024; Ogledov: 0; Prenosov: 6
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6. Synchronization in simplicial complexes of memristive Rulkov neuronsMahtab Mehrabbeik, Sajad Jafari, Matjaž Perc, 2023, izvirni znanstveni članek Opis: Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.
Ključne besede: simplicial complex, higher-order network, memristive Rulkov, synchronization, cluster synchronization
Objavljeno v DKUM: 11.09.2024; Ogledov: 37; Prenosov: 9
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7. Swarmalators under competitive time-varying phase interactionsGourab Kumar Sar, Sayantan Nag Chowdhury, Matjaž Perc, Dibakar Ghosh, 2022, izvirni znanstveni članek Opis: Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractive–repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static π, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuart–Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling.
Ključne besede: swarmalators, time-varying couplings, synchronization, competitive phase coupling
Objavljeno v DKUM: 16.07.2024; Ogledov: 87; Prenosov: 12
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8. Interlayer and intralayer synchronization in multiplex fractional-order neuronal networksBo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2022, izvirni znanstveni članek Opis: Fractional-order models describing neuronal dynamics often exhibit better compatibility with diverse neuronal firing patterns that can be observed experimentally. Due to the overarching significance of synchronization in neuronal dynamics, we here study synchronization in multiplex neuronal networks that are composed of fractional-order Hindmarsh-Rose neurons. We compute the average synchronization error numerically for different derivative orders in dependence on the strength of the links within and between network layers. We find that, in general, fractional-order models synchronize better than integer-order models. In particular, we show that the required interlayer and intralayer coupling strengths for interlayer or intralayer synchronization can be weaker if we reduce the derivative order of the model describing the neuronal dynamics. Furthermore, the dependence of the interlayer or intralayer synchronization on the intralayer or interlayer coupling strength vanishes with decreasing derivative order. To support these results analytically, we use the master stability function approach for the considered multiplex fractional-order neuronal networks, by means of which we obtain sufficient conditions for the interlayer and intralayer synchronizations that are in agreement with numerical results.
Ključne besede: synchronization, neuronal network, multilayer network, neuronal dynamics
Objavljeno v DKUM: 28.05.2024; Ogledov: 230; Prenosov: 8
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9. Disinhibition-induced transitions between absence and tonic-clonic epileptic seizuresDenggui Fan, Qingyun Wang, Matjaž Perc, 2015, izvirni znanstveni članek Opis: Electrophysiological experiments have long revealed the existence of two-way transitions between absence and tonic-clonic epileptic seizures in the cerebral cortex. Based on a modified spatially-extended Taylor & Baier neural field model, we here propose a computational framework to mathematically describe the transition dynamics between these epileptic seizures. We first demonstrate the existence of various transition types that are induced by disinhibitory functions between two inhibitory variables in an isolated Taylor & Baier model. Moreover, we show that these disinhibition-induced transitions can lead to stable tonic-clonic oscillations as well as periodic spike with slow-wave discharges, which are the hallmark of absence seizures. We also observe fascinating dynamical states, such as periodic 2-spike with slow-wave discharges, tonic death, bursting oscillations, as well as saturated firing. Most importantly, we identify paths that represent physiologically plausible transitions between absence and tonic-clonic seizures in the modified spatially-extended Taylor & Baier model.
Ključne besede: epilepsy, neuronal dynamics, synchronization, biophysics
Objavljeno v DKUM: 23.06.2017; Ogledov: 1181; Prenosov: 372
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10. Basin stability for chimera statesSarbendu Rakshit, Bidesh Bera, Matjaž Perc, Dibakar Ghosh, 2017, izvirni znanstveni članek Opis: Chimera states, namely complex spatiotemporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics, are investigated in a network of coupled identical oscillators. These intriguing spatiotemporal patterns were first reported in nonlocally coupled phase oscillators, and it was shown that such mixed type behavior occurs only for specific initial conditions in nonlocally and globally coupled networks. The influence of initial conditions on chimera states has remained a fundamental problem since their discovery. In this report, we investigate the robustness of chimera states together with incoherent and coherent states in dependence on the initial conditions. For this, we use the basin stability method which is related to the volume of the basin of attraction, and we consider nonlocally and globally coupled time-delayed Mackey-Glass oscillators as example. Previously, it was shown that the existence of chimera states can be characterized by mean phase velocity and a statistical measure, such as the strength of incoherence, by using well prepared initial conditions. Here we show further how the coexistence of different dynamical states can be identified and quantified by means of the basin stability measure over a wide range of the parameter space.
Ključne besede: synchronization, oscillations, symmetry breaking, network
Objavljeno v DKUM: 23.06.2017; Ogledov: 1274; Prenosov: 366
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