arXiv subjects

Jakub Sawicki

Publications and source records attributed to Jakub Sawicki.

At least 19 recordsLinked to original sources

arXiv2025

Synchronisation zweier Labialpfeifen

The synchronization of coupled organ pipes represents a nonlinear phenomenon. The investigation of synchronization effects in organ pipes using a model of time-delayed coupled Van der Pol oscillators shows that synchronization improves pitch stability but can also lead to sound attenuation. The Arnold tongue illustrates the influence of distance-dependent coupling on stability and frequency adaptation. The results agree qualitatively well with experiments and emphasize the relevance of nonlinear coupling mechanisms in organ acoustics. -- Die Synchronisation gekoppelter Orgelpfeifen stellt ein nichtlineares Ph{ä}nomen dar. Die Untersuchung von Synchronisationseffekten bei Orgelpfeifen anhand eines Modells zeitverz{ö}gert gekoppelter Van-der-Pol-Oszillatoren zeigt, dass Synchronisation die Tonh{ö}henstabilit{ä}t verbessert, aber auch zu Schalld{ä}mpfung f{ü}hren kann. Die Arnold-Zunge verdeutlicht den Einfluss distanzabh{ä}ngiger Kopplung auf Stabilit{ä}t und Frequenzanpassung. Die Ergebnisse stimmen qualitativ gut mit Experimenten {ü}berein und betonen die Relevanz nichtlinearer Kopplungsmechanismen in der Orgelakustik.

nlin.AO↗

arXiv2025

From empirical brain networks towards modeling music perception -- a perspective

This perspective article investigates how auditory stimuli influence neural network dynamics using the FitzHugh-Nagumo (FHN) model and empirical brain connectivity data. Results show that synchronization is sensitive to both the frequency and amplitude of auditory input, with synchronization enhanced when input frequencies align with the system's intrinsic frequencies. Increased stimulus amplitude broadens the synchronization range governed by a delicate interplay involving the network's topology, the spatial location of the input, and the frequency characteristics of the cortical input signals. This perspective article also reveals that brain activity alternates between synchronized and desynchronized states, reflecting critical dynamics and phase transitions in neural networks. Notably, gamma-band synchronization is crucial for processing music, with coherence peaking in this frequency range. The findings emphasize the role of structural connectivity and network topology in modulating synchronization, providing insights into how music perception engages brain networks. This perspective article offers a computational framework for understanding neural mechanisms in music perception, with potential implications for cognitive neuroscience and music psychology.

q-bio.NC↗

arXiv2025

Adaptation and synchronization -- basic mechanisms in music performance

This review examines the roles of adaptation and synchronization in music performance, drawing on concepts from complex systems theory to understand the dynamic interactions between musicians, music, and listeners. Adaptation is explored through how musicians adjust their cognitive, emotional, and motor systems across the stages of preparation, execution, and reception, while synchronization is emphasized as essential for aligning internal states, coordinating actions with other performers, and engaging with the audience. The review highlights the interdisciplinary nature of music performance research, integrating cognitive, motor, and emotional processes to enhance both individual and collective musical expression. It also addresses the psychological state of flow, which arises from synchronized neurocognitive mechanisms that optimize performance. Additionally, the emotional synchronization facilitated by music is explored, emphasizing its role in both individual emotional coherence and social coordination within musical ensembles. Finally, the review highlights recent findings on interpersonal and inter-brain synchronization, particularly in live music performances and improvisation, showing how synchronization fosters creativity, social cohesion, and a shared collective experience.

physics.soc-ph↗

arXiv2025

Importance of near- and far-field coupling for the synchronization of organ pipes

The synchronization of coupled organ pipes represents a nonlinear phenomenon with significant implications for both musical acoustics and nonlinear dynamics. This study investigates the coupling mechanisms governing synchronization, employing a theoretical framework based on delay-coupled Van der Pol oscillators. The oscillatory behavior of individual organ pipes is modeled as a self-sustained system driven by an air jet interacting with the pipe resonator. By incorporating experimental data and numerical simulations, we analyze the impact of finite separation between coupled pipes, introducing time-delayed interactions in the coupling function. Our findings reveal that synchronization can enhance pitch stability but may also induce sound attenuation due to destructive interference, particularly in prospect pipes. A key focus of this study is the decomposition of the coupling mechanism into near-field and far-field components, each contributing differently to the overall synchronization dynamics. Through bifurcation analysis and Arnold tongue characterization, we demonstrate how distance-dependent interactions influence the stability and frequency locking of coupled oscillators. The Fast Fourier Transform (FFT) is employed to extract spectral features from numerical data, ensuring precise comparison with experiments. Our results show strong qualitative agreement between modeled and observed synchronization effects, highlighting the importance of nonlinear coupling in organ pipe acoustics. This investigation advances the understanding of mutual interactions in coupled acoustic oscillators and provides a refined theoretical basis for predicting synchronization phenomena in complex aerodynamically driven systems.

nlin.AO↗

arXiv2024

Interplay of synchronization and cortical input in models of brain networks

It is well known that synchronization patterns and coherence have a major role in the functioning of brain networks, both in pathological and in healthy states. In particular, in the perception of sound, one can observe an increase in coherence between the global dynamics in the network and the auditory input. In this perspective article, we show that synchronization scenarios are determined by a fine interplay between network topology, the location of the input, and frequencies of these cortical input signals. To this end, we analyze the influence of an external stimulation in a network of FitzHugh-Nagumo oscillators with empirically measured structural connectivity, and discuss different areas of cortical stimulation, including the auditory cortex.

nlin.AO↗

arXiv2023

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges, and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

nlin.AO↗

arXiv2022

Modelling the perception of music in brain network dynamics

We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report an increase of coherence between the global dynamics in our network and the input signal induced by a specific music song. We show that the level of coherence depends crucially on the frequency band. We compare our results with experimental data, which also describe global neural synchronization between different brain regions in the gamma-band range and its increase just before transitions between different parts of the musical form (musical high-level events). The results also suggest a separation in musical form-related brain synchronization between high brain frequencies, associated with neocortical activity, and low frequencies in the range of dance movements, associated with interactivity between cortical and subcortical regions.

nlin.AO↗

arXiv2022

Critical parameters in dynamic network modeling of sepsis

In this work, we propose a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences. We develop a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the coevolutionary dynamics of parenchymal, immune cells, and cytokines. By means of the simple paradigmatic model of phase oscillators in a two-layer system, we analyze the emergence of organ threatening interactions between the dysregulated immune system and the parenchyma. We demonstrate that the complex cellular cooperation between parenchyma and stroma (immune layer) either in the physiological or in the pathological case can be related to dynamical patterns of the network. In this way we explain sepsis by the dysregulation of the healthy homeostatic state (frequency synchronized) leading to a pathological state (desynchronized or multifrequency cluster) in the parenchyma. We provide insight into the complex stabilizing and destabilizing interplay of parenchyma and stroma by determining critical interaction parameters. The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (response of the innate immune system) is represented by nodes of a duplex layer. Cytokine interaction is modeled by adaptive coupling weights between nodes representing immune cells (with fast adaptation timescale) and parenchymal cells (slow adaptation timescale), and between pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). The proposed model allows for a functional description of organ dysfunction in sepsis and the recurrence risk in a plausible pathophysiological context.

nlin.AO↗

arXiv2021

Modeling tumor disease and sepsis by networks of adaptively coupled phase oscillators

In this study, we provide a dynamical systems perspective to the modelling of pathological states induced by tumors or infection. A unified disease model is established using the innate immune system as the reference point. We propose a two-layer network model for carcinogenesis and sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the co-evolutionary dynamics of parenchymal, immune cells, and cytokines. Our aim is to show that the complex cellular cooperation between parenchyma and stroma (immune layer) in the physiological and pathological case can be qualitatively and functionally described by a simple paradigmatic model of phase oscillators. By this, we explain carcinogenesis, tumor progression, and sepsis by destabilization of the healthy homeostatic state (frequency synchronized), and emergence of a pathological state (desynchronized or multifrequency cluster). The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (reaction of innate immune system) are represented by nodes of a duplex layer. The cytokine interaction is modeled by adaptive coupling weights between the nodes representing the immune cells (with fast adaptation time scale) and the parenchymal cells (slow adaptation time scale) and between the pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). Thereby, carcinogenesis, organ dysfunction in sepsis, and recurrence risk can be described in a correct functional context.

nlin.AO↗

arXiv2021

Synchronization scenarios in three-layer networks with a hub

We study various relay synchronization scenarios in a three-layer network, where the middle (relay) layer is a single node, i.e. a hub, The two remote layers consist of non-locally coupled rings of FitzHugh-Nagumo oscillators modelling neuronal dynamics. All nodes of the remote layers are connected to the hub. The role of the hub and its importance for the existence of chimera states is investigated in dependence on the inter-layer coupling strength and inter-layer time delay. Tongue-like regions in the parameter plane exhibiting double chimeras, i.e., chimera states in the remote layers whose coherent cores are synchronized with each other, and salt-and-pepper states are found. At very low intra-layer coupling strength, when chimera states do not exist in single layers, these may be induced by the hub. Also the influence of dilution of links between the remote layers and the hub upon the dynamics is investigated. The greatest effect of dilution is observed when links to the coherent domain of the chimeras are removed.

nlin.AO↗

arXiv2021

Influence of sound on empirical brain networks

We analyze the influence of an external sound source in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the sound source. We show that the level of synchrony can be enhanced by choosing the frequency of the sound source and its amplitude as control parameters for synchronization patterns. We discuss a minimum model elucidating the modalities of the influence of music on the human brain.

nlin.AO↗

arXiv2020

Effect of Topology upon Relay Synchronization in Triplex Neuronal Networks

Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three-layer networks of interacting FitzHugh-Nagumo oscillators. We demonstrate that the phenomenon of relay synchronization is robust to topological random inhomogeneities of small-world type in the layer networks. We show that including randomness in the connectivity structure either of the remote network layers, or of the relay layer, increases the range of interlayer coupling strength where relay synchronization can be observed.

nlin.AO↗

arXiv2019

Birth and stabilization of phase clusters by multiplexing of adaptive networks

We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multi-layer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.

nlin.AO↗

arXiv2019

Approximation of the objective insensitivity regions using Hierarchic Memetic Strategy coupled with Covariance Matrix Adaptation Evolutionary Strategy

One of the most challenging types of ill-posedness in global optimization is the presence of insensitivity regions in design parameter space, so the identification of their shape will be crucial, if ill-posedness is irrecoverable. Such problems may be solved using global stochastic search followed by post-processing of a local sample and a local objective approximation. We propose a new approach of this type composed of Hierarchic Memetic Strategy (HMS) powered by the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) well-known as an effective, self-adaptable stochastic optimization algorithm and we leverage the distribution density knowledge it accumulates to better identify and separate insensitivity regions. The results of benchmarks prove that the improved HMS-CMA-ES strategy is effective in both the total computational cost and the accuracy of insensitivity region approximation. The reference data for the tests was obtained by means of a well-known effective strategy of multimodal stochastic optimization called the Niching Evolutionary Algorithm 2 (NEA2), that also uses CMA-ES as a component.

cs.NE↗

arXiv2019

Partial synchronization in empirical brain networks as a model for unihemispheric sleep

We analyze partial synchronization patterns in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report a dynamical asymmetry between the hemispheres, induced by the natural structural asymmetry. We show that the dynamical asymmetry can be enhanced by introducing the inter-hemispheric coupling strength as a control parameter for partial synchronization patterns. We specify the possible modalities for existence of unihemispheric sleep in human brain, where one hemisphere sleeps while the other remains awake. In fact, this state is common among migratory birds and mammals like aquatic species.

nlin.AO↗

arXiv2019

Relay synchronization in multiplex networks of discrete maps

Complex multiplex networks consist of several subnetwork layers, which interact via pairwise inter-layer connections. Relay synchronization between distant layers which are not directly connected, but only via a relay layer, can be observed in multiplex networks. We study three-layer networks of discrete logistic maps, where each individual layer is a nonlocally coupled ring, and demonstrate scenarios of relay synchronization of complex patterns in the outer layers which interact via an intermediate layer. We find regimes of relay synchronization for chimera states, i.e., patterns of coexisting coherent and incoherent domains, and a transition from phase chimeras to amplitude chimeras for increasing inter-layer coupling. We determine analytically the approximate critical coupling strengths for the existence of phase chimeras.

nlin.AO↗

arXiv2018

Delay-induced chimeras in neural networks with fractal topology

We study chimera states, which are partial synchronization patterns consisting of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics, in ring networks of FitzHugh-Nagumo oscillators with fractal connectivities. In particular, we focus on the interplay of time delay in the coupling term and the network topology. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of coherent dynamics. We show analytically and numerically that the period of the synchronized dynamics as a function of delay is characterized by a sequence of piecewise linear branches. In between these branches various chimera states and other partial synchronization patterns are induced by the time delay. By varying the time delay one can deliberately choose and stabilize desired spatio-temporal patterns.

nlin.AO↗

arXiv2018

Delay controls chimera relay synchronization in multiplex networks

We study remote (or relay) synchronization in multilayer networks between parts of one layer and their counterparts in a second layer, where these two layers are not directly connected. A simple realization of such a system is a triplex network where a relay layer in the middle, which is generally not synchronized, acts as a transmitter between two outer layers. We establish time delay in the inter-layer coupling as a powerful tool to control various partial synchronization patterns, in particular chimera states, i.e., complex patterns of coexisting coherent and incoherent domains. We demonstrate that the three-layer structure of the network allows for synchronization of the coherent domains of chimera states in the first layer with their counterparts in the third layer, whereas the incoherent domains either remain desynchronized or synchronized. By varying the topology of the relay layer, we study its influence on the remote synchronization in the outer layers. As model dynamics we use the paradigmatic FitzHugh-Nagumo system.

nlin.AO↗