1. Dynamics on higher-order networks: a reviewSoumen Majhi, Matjaž Perc, Dibakar Ghosh, 2022, review article Abstract: 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.
Keywords: higher-order networks, synchronization, cooperation, dynamics
Published in DKUM: 17.09.2024; Views: 0; Downloads: 0 |
2. Synchronization in simplicial complexes of memristive Rulkov neuronsMahtab Mehrabbeik, Sajad Jafari, Matjaž Perc, 2023, original scientific article Abstract: 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.
Keywords: simplicial complex, higher-order network, memristive Rulkov, synchronization, cluster synchronization
Published in DKUM: 11.09.2024; Views: 37; Downloads: 8
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3. Swarmalators under competitive time-varying phase interactionsGourab Kumar Sar, Sayantan Nag Chowdhury, Matjaž Perc, Dibakar Ghosh, 2022, original scientific article Abstract: 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.
Keywords: swarmalators, time-varying couplings, synchronization, competitive phase coupling
Published in DKUM: 16.07.2024; Views: 87; Downloads: 10
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4. Interlayer and intralayer synchronization in multiplex fractional-order neuronal networksBo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2022, original scientific article Abstract: 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.
Keywords: synchronization, neuronal network, multilayer network, neuronal dynamics
Published in DKUM: 28.05.2024; Views: 230; Downloads: 0 |
5. Disinhibition-induced transitions between absence and tonic-clonic epileptic seizuresDenggui Fan, Qingyun Wang, Matjaž Perc, 2015, original scientific article Abstract: 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.
Keywords: epilepsy, neuronal dynamics, synchronization, biophysics
Published in DKUM: 23.06.2017; Views: 1181; Downloads: 366
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6. Basin stability for chimera statesSarbendu Rakshit, Bidesh Bera, Matjaž Perc, Dibakar Ghosh, 2017, original scientific article Abstract: 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.
Keywords: synchronization, oscillations, symmetry breaking, network
Published in DKUM: 23.06.2017; Views: 1274; Downloads: 357
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7. Synchronous bursts on scale-free neuronal networks with attractive and repulsive couplingQingyun Wang, Guanrong Chen, Matjaž Perc, 2011, original scientific article Abstract: This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.
Keywords: synchronization, neuronal networks, noise, stochastic processes, scale-free networks, information transmission delay
Published in DKUM: 19.06.2017; Views: 1218; Downloads: 386
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8. Gap junctions and epileptic seizures - two sides of the same coin?Vladislav Volman, Matjaž Perc, Maxim Bazhenov, 2011, original scientific article Abstract: Electrical synapses (gap junctions) play a pivotal role in the synchronization of neuronal ensembles which also makes them likely agonists of pathological brain activity. Although large body of experimental data and theoretical considerations indicate that coupling neurons by electrical synapses promotes synchronous activity (and thus is potentially epileptogenic), some recent evidence questions the hypothesis of gap junctions being among purely epileptogenic factors. In particular, an expression of inter-neuronal gap junctions is often found to be higher after the experimentally induced seizures than before. Here we used a computational modeling approach to address the role of neuronal gap junctions in shaping the stability of a network to perturbations that are often associated with the onset of epileptic seizures. We show that under some circumstances, the addition of gap junctions can increase the dynamical stability of a network and thus suppress the collective electrical activity associated with seizures. This implies that the experimentally observed post-seizure additions of gap junctions could serve to prevent further escalations, suggesting furthermore that they are a consequence of an adaptive response of the neuronal network to the pathological activity. However, if the seizures are strong and persistent, our model predicts the existence of a critical tipping point after which additional gap junctions no longer suppress but strongly facilitate the escalation of epileptic seizures. Our results thus reveal a complex role of electrical coupling in relation to epileptiform events. Which dynamic scenario (seizure suppression or seizure escalation) is ultimately adopted by the network depends critically on the strength and duration of seizures, in turn emphasizing the importance of temporal and causal aspects when linking gap junctions with epilepsy.
Keywords: epilepsy, nonlinear dynamics, electrical synapses, coupling, synchronization
Published in DKUM: 19.06.2017; Views: 1119; Downloads: 413
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9. LANGUAGE VARIETIES IN THE SYNCHRONIZATION OF THE FILMS MADAGASCAR 3 AND OPEN SEASONMaruša Babič, 2015, undergraduate thesis Abstract: This graduation thesis, entitled Language varieties in the synchronization of the films Madagascar 3 and Open season, consists of two main parts. The theoretical part defines synchronization as a form of audiovisual translation and focuses on the synchronization of animated films. Animated films are made mostly for the youngest viewers, therefore the subject of translating for children is examined. The language varieties of Slovene and English language are described, since there are different dialects represented in the analyzed animated films. The second part focuses on the empirical research, where the language varieties in the synchronization of the animated films Madagascar 3 and Open season are analyzed. The film speech was transcribed for the purpose to conduct the analysis of the language varieties. The prevailing speech variety is colloquial Standard Slovene with the features of colloquial language of Ljubljana. The linguistic features of the main characters were identified and it was investigated how they affect characterization process. Since both films originate from American culture, an analysis of the translation culture-specific and idiomatic expressions was also implemented. The aim of this graduation thesis is to analyze language varieties in the synchronization of the films and investigate whether colloquial language of Ljubljana is used more than other regional colloquial varieties.
Keywords: synchronization, animated film, translating for children, language varieties, colloquial language, translating culture-specific terms
Published in DKUM: 05.06.2015; Views: 1985; Downloads: 113
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