1. Synchronization stability in simplicial complexes of near-identical systemsFatemeh Parastesh, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, Charo I. del Genio, Stefano Boccaletti, 2025, izvirni znanstveni članek Opis: Assessing the stability of synchronization is a fundamental task when studying networks of dynamical systems. However, this becomes challenging when the coupled systems are not exactly identical, as is al ways the case in practical settings. Here we introduce an extension of the Master Stability Function to determine near-synchronization stability within simplicial complexes of nearly identical systems coupled by synchronization-noninvasive functions. We validate our method on a simplicial complex of Lorenz oscillators, f inding a good correspondence between the predicted regions of stability and those observed via direct simula tion. This confirms the correctness of our approach, making it a valuable tool for the evaluation of real-world systems, in which differences between the constitutive elements are unavoidable.
Ključne besede: chaos, collective dynamics, coupled oscillators, dynamics of networks, synchronization, chaotic systems, dynamical systems, networks
Objavljeno v DKUM: 10.07.2025; Ogledov: 0; Prenosov: 11
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2. 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: 431
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3. 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: 13
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