Collective Dynamics Research Articles

Deeper but smaller: Higher-order interactions increase linear stability but shrink basins.

A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known about how higher-order interactions shape the global organization of different states. Here, we shed light on this issue by analyzing the rich patterns supported by identical Kuramoto oscillators on hypergraphs. We show that higher-order interactions can have opposite effects on linear stability and basin stability: They stabilize twisted states (including full synchrony) by improving their linear stability, but also make them hard to find by markedly reducing their basin size. Our results highlight the importance of understanding higher-order interactions from both local and global perspectives.

Unraveling polarization: insights into individual and collective dynamics.

Polarization poses a critical threat to the stability of nations around the world, as it impacts climate change, populism, democracy, and global health. This perspective examines the conceptual understanding, measurement challenges, and potential interventions for polarization. Our analysis highlights the distinction and interactions between the individual and collective levels of polarization, conceptually, methodologically, and in terms of interventions. We conclude by pointing out future directions for understanding polarization and highlighting the interrelations between polarization and other social phenomena.

Synchronization and limit cycles in a simple contagion model with time delays

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N−asset models with appropriate parameterization.

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Unravelling a diversity of cellular structures and aggregation dynamics during the early development of Myxococcus xanthus.

Aggregation underlies the collective dynamics of a diversity of organisms, enabling the formation of complex structures and emergent behaviours on interaction with the environment. Cellular aggregation constitutes one of the routes to collective motility and multicellular development. Myxococcus xanthus, a social bacterium, is a valuable model for studying the aggregative path to multicellularity, a major transition in the evolutionary history of life. While the collective developmental behaviour of M. xanthus has been largely studied in high cellular densities, there is a lack of understanding at low-density conditions that can be ecologically relevant. In this work, we study the early stages of emergent collective behaviour of M. xanthus under nutrient-poor and low-density conditions, uncovering the formation of diverse cellular structures with different shapes and sizes, ranging from individual cells to networks comprising thousands of cells. We study their motility patterns and their prevalence along development and discuss their cross-scale role on the population's exploratory dynamics. This work contributes to understanding key, yet largely understudied, aspects in the early stages of multicellular development in myxobacteria, shedding light on the dynamics underlying aggregative processes in this and other taxa and study systems.

Tipping prediction of a class of large-scale radial-ring neural networks

Understanding the emergence and evolution of collective dynamics in large-scale neural networks remains a complex challenge. This paper seeks to address this gap by applying dynamical systems theory, with a particular focus on tipping mechanisms. First, we introduce a novel (n+mn)-scale radial-ring neural network and employ Coates’ flow graph topological approach to derive the characteristic equation of the linearized network. Second, through deriving stability conditions and predicting the tipping point using an algebraic approach based on the integral element concept, we identify critical factors such as the synaptic transmission delay, the self-feedback coefficient, and the network topology. Finally, we validate the methodology’s effectiveness in predicting the tipping point. The findings reveal that increased synaptic transmission delay can induce and amplify periodic oscillations. Additionally, the self-feedback coefficient and the network topology influence the onset of tipping points. Moreover, the selection of activation function impacts both the number of equilibrium solutions and the convergence speed of the neural network. Lastly, we demonstrate that the proposed large-scale radial-ring neural network exhibits stronger robustness compared to lower-scale networks with a single topology. The results provide a comprehensive depiction of the dynamics observed in large-scale neural networks under the influence of various factor combinations.

Behavioral swarms: A mathematical theory toward swarm intelligence

This paper presents a mathematical theory of behavioral swarms, where the state of interacting entities, which are called active particles, includes in addition to position and velocity, an internal variable, called activity, which has the ability to interact with mechanical variables thus affecting the interaction rules. In turn, the mechanical variables can modify the dynamics of activity variable. This approach is useful for describing the dynamics of living systems with a finite number of interacting entities. This paper provides a general conceptual framework that extends the pioneering work [N. Bellomo, S.-Y. Ha and N. Outada, Towards a mathematical theory of behavioral swarms, ESAIM: Control Theory Var. Calculus 26 (2020) 125, https://doi.org/10.1051/cocv/2020071 ]. The theory is firstly developed for the constant number of active particles. Then, it is considered for the case of particles tending to infinity. This theory is useful for describing the dynamics of living systems. Therefore, it provides the conceptual basis for developing a mathematical theory of behavioral swarms, which naturally lead to the study of a theory of swarm intelligence. A study of the dynamics of swarms shows how the theory can be applied to real world collective dynamics.

Percolation versus depinning transition: The inherent role of damage hardening during quasibrittle failure.

The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well described by scaling laws. In deciphering its origins, failure is routinely interpreted as a critical transition. However at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with the strength of disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the microfracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure but also affect the preceding damage accumulation. When hardening is low, the precursory activity is strongly influenced by the strength of the disorder and is reminiscent of damage percolation. On the contrary, for large hardening, long-range elastic interactions prevail over disorder, ensuring a rather homogeneous evolution of the damage field in the material. The power-law statistics of the damage bursts is robust to the strength of the disorder and is reminiscent of the collective avalanche dynamics of elastic interfaces near the depinning transition. The existence of these two distinct universality classes also manifests as different values of the scaling exponent characterizing the divergence of the precursor size on approaching failure. Our finding sheds new light on the connection between the level of quasibrittleness of materials and the statistical features of the failure precursors. Finally, it also provides a more complete description of the acoustic precursors and thus paves the way for quantitative techniques of damage monitoring of structures-in-service.

Intrinsic statistical regularity of topological charges revealed in dynamical disk model.

Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive particles confined on a disk under the Hamiltonian dynamics by the recently developed algorithm called the random batch method. This algorithm is specifically designed for reducing the computational complexity of long-range interacting particle systems. We highlight the revealed intrinsic statistical regularity of topological charges that is otherwise unattainable by the continuum analysis of particle density. We also identify distinct collective dynamics of the interacting particles under short- and long-range repulsive forces. This work shows the robustness and effectiveness of the concept of topological charge for characterizing the convoluted particle dynamics, and itdemonstrates the promising potential of the random batch method for exploring fundamental scientific questions arising in a variety of long-range interacting particle systems in soft matter physics and other relevant fields.

Inside-out and outside-in: How entrepreneurial ecosystems can build legitimacy through signaling

ABSTRACT The entrepreneurial ecosystem is increasingly drawing the attention of scholars and practitioners, underscoring the importance of collective dynamics between entrepreneurs and entrepreneurial-support intermediaries in fostering entrepreneurial activity. The entrepreneurial journey is characterized by information asymmetry, with entrepreneurial actors sending signals as representations of their underlaying qualities, hoping to acquire necessary resources. Current entrepreneurship research predominantly applies signaling theory to individual and venture-level activities. However, studies that explore signaling within the broader context of entrepreneurial ecosystems are scarce. This paper aims to bridge the entrepreneurial ecosystem-signaling gap by offering insight into how emerging entrepreneurial ecosystems gain legitimacy. We analyze a nascent, privately governed entrepreneurial ecosystem located in Valencia, Spain. Employing a conceptual model based on our findings, we introduce a key boundary condition for the study of signaling in an entrepreneurship context.

Supramolecular Arrangement and Conformational and Dynamic Properties of Chiral Smectic Liquid Crystals Obtained through Nuclear Magnetic Resonance: A Brief Review

Ferroelectric and antiferroelectric smectic liquid crystalline (LC) phases are still at the center of investigations and interests for both their fundamental properties and variety of technological applications. This review aims to report the main contributions based on different nuclear magnetic resonance (NMR) techniques to the study of chiral liquid crystalline calamitic mesogens forming smectic phases, such as the SmA, the SmC* (ferroelectric), and the SmC*A (antiferroelectric) phases. 2H NMR and 13C NMR techniques and their combination were of help in clarifying the local orientational properties (i.e., the molecular and fragments’ main orientational order parameters) at the transition between the SmA and the SmC* phases, and in the particular case of de Vries liquid crystals, NMR studies gave important clues regarding the actual models describing the molecular arrangement in these two phases formed by de Vries LCs. Moreover, this review describes how the combination of 2H NMR relaxation times’ analysis, 1H NMR relaxometry, and 1H NMR diffusometry was successfully applied to the study of chiral smectogens forming the SmC* and SmC*A phases, with the determination of relevant parameters describing both rotational molecular and internal motions, collective dynamics, and translational self-diffusion motions. Several cases will be reported concerning NMR investigations of chiral ferroelectric and antiferroelectric phases, underlining the great potential of combined NMR approaches to the study of supramolecular, conformational, and dynamic properties of liquid crystals.

Emergence of subharmonics in a microwave driven dissipative Rydberg gas

Quantum many-body systems near phase transitions respond collectively to externally applied perturbations. We explore this phenomenon in a laser-driven dissipative Rydberg gas that is tuned to a bistable regime. Here two metastable phases coexist, which feature a low and high density of Rydberg atoms, respectively. The ensuing collective dynamics, which we monitor , is characterized by stochastic collective jumps between these two macroscopically distinct many-body phases. We show that the statistics of these jumps can be controlled using a dual-tone microwave field. In particular, we find that the distribution of jump times develops peaks corresponding to subharmonics of the relative microwave detuning. Our study demonstrates the control of collective statistical properties of dissipative quantum many-body systems without the necessity of fine-tuning or of ultracold temperatures. Such robust many-body phenomena may find technological applications in sensing. Published by the American Physical Society 2024

Effect of anisotropy on the formation of heavy quarkonium bound states

We study the real part of the static potential of a heavy quark-antiquark system in an anisotropic plasma medium. We use a quasiparticle approach where the collective dynamics of the plasma constituents is described using hard-loop perturbation theory. The parton distribution function is characterized by a set of parameters that can accurately describe the anisotropy of the plasma produced in a heavy ion collision. We calculate the potential numerically in strongly anisotropic systems and study the angular dependence of the distortion of the potential relative to the isotropic one. We obtain an analytic expression for the real part of the heavy quark potential in the limit of weak anisotropy using a model that expresses the potential in terms of effective screening masses that depend on the anisotropy parameters and the orientation of the quark-antiquark pair. A one-dimensional potential is formulated in terms of angle averaged screening masses that incorporate the anisotropy of the medium into a radial coordinate. We solve the corresponding Schrödinger equation and show that the magnitude of the binding energy typically increases with anisotropy. Anisotropy can play an important role, especially in states with nonzero angular momentum. This means that the number of bound states that are formed could depend on specific characteristics of the anisotropy of the plasma. Our study suggests that plasma anisotropy plays an important role in the dynamics of heavy quarkonium and motivates further study. Published by the American Physical Society 2024

Unraveling abnormal collective effects via the non-monotonic number dependence of electron transfer in confined electromagnetic fields.

Strong light-matter coupling within an optical cavity leverages the collective interactions of molecules and confined electromagnetic fields, giving rise to the possibilities of modifying chemical reactivity and molecular properties. While collective optical responses, such as enhanced Rabi splitting, are often observed, the overall effect of the cavity on molecular systems remains ambiguous for a large number of molecules. In this paper, we investigate the non-adiabatic electron transfer process in electron donor-acceptor pairs influenced by collective excitation and local molecular dynamics. Using the timescale difference between reorganization and thermal fluctuations, we derive analytical formulas for the electron transfer rate constant and the polariton relaxation rate. These formulas apply to any number of molecules (N) and account for the collective effect as induced by cavity photon coupling. Our findings reveal a non-monotonic dependence of the rate constant on N, which can be understood by the interplay between electron transfer and polariton relaxation. As a result, the cavity-induced quantum yield increases linearly with N for small N (as predicted by a simple Dicke model) but shows a turnover and suppression for large N. We also interrelate the thermal bath frequency and the number of molecules, suggesting the optimal number for maximizing enhancement. The analysis provides an analytical insight for understanding the collective excitation of light and electron transfer, helping to predict the optimal condition for effective cavity-controlled chemical reactivity.

Aging transitions of multimodal oscillators in multilayer networks

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. Published by the American Physical Society 2024

Rosetta stone for the population dynamics of spiking neuron networks.

Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equilibrium. Despite its general applicability, the Fokker-Planck equationgoverning such evolution is mainly studied within the borders of the linear response theory, although alternative spectral expansion approaches offer some advantages in the study of the out-of-equilibrium dynamics. This is mainly due to the difficulty in computing the state-dependent coefficients of the expanded system of differential equations. Here, we address this issue by deriving analytic expressions for such coefficients by pairing perturbative solutions of the Fokker-Planck approach with their counterparts from the spectral expansion. A tight relationship emerges between several of these coefficients and the Laplace transform of the interspike interval density (i.e., the distribution of first-passage times). "Coefficients" like the current-to-rate gain function, the eigenvalues of the Fokker-Planck operator and its eigenfunctions at the boundaries are derived without resorting to integral expressions. For the leaky integrate-and-fire neurons, the coupling terms between stationary and nonstationary modes are also worked out paving the way to accurately characterize the critical points and the relaxation timescales in networks of interacting populations.

Non-Markovian collective emission of giant emitters in the Zeno regime

We explore the collective Zeno dynamics of giant artificial atoms that are coupled, via multiple coupling points, to a common photonic or acoustic reservoir. In this regime, the establishment of atomic cooperativity and the revivification of exponential decay are highly intertwined, which is utterly beyond the non-Markovian regime with only retarded backaction. We reveal that giant atoms build up their collective emission smoothly from the decay rate of zero to that predicted by Markovian approximation and show great disparity between different waveguide QED setups. As a comparison, the steplike growth of instantaneous decay rates in the retardation-only picture has also been shown. All of these theoretical pictures predict the same collective behavior in the long time limit. From a phenomenological standpoint, we observe that the atomic superradiance exhibits significant directional property. In addition, the subradiant photons feature prolonged oscillation in the early stage of collective radiance, where the energy is exchanged remarkably between giant emitters and the field. Our results might be probed in state-of-art waveguide QED experiments and fundamentally broaden the fields of collective emission in systems with giant atoms. Published by the American Physical Society 2024

From case study to general principle: An analysis of the development mechanism and policy optimization of mangrove carbon sinks

Mangroves, as a crucial coastal ecosystem, possess significant carbon sink functions and play a key role in mitigating global climate change. This paper, based on the Zhanjiang Mangrove Afforestation Project in Guangdong, explores the development mechanisms and economic and ecological benefits of mangrove carbon sink projects through the lens of collective action theory and system dynamics modeling. The study finds that the primary reason for the unsustainable progression of mangrove carbon sink projects is the lack of intrinsic motivation among local villagers to engage in collective action. By constructing a system dynamics model, this paper quantifies the long-term impacts of mangrove carbon sink projects on local socio-economic welfare and proposes policy optimization recommendations. These recommendations include expanding income sources for local villagers, establishing carbon trading and ecological compensation mechanisms, and involving international non-governmental organizations. The findings of this study not only provide guidance for mangrove carbon sink projects in China but also offer valuable insights for the promotion of similar projects globally.

Non-local interaction in discrete Ricci curvature-induced biological aggregation

We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman–Ricci curvature.

The part and the whole: how single nodes contribute to large-scale phase-locking in functional EEG networks

ObjectiveThe application of signal analysis techniques to electroencephalographic (EEG) recordings from epilepsy patients shows that epilepsy involves not only altered neuronal synchronization but also the reorganization of functional EEG networks. This study aims to assess the large-scale phase-locking of such functional networks and how individual network nodes contribute to this collective dynamics. MethodsWe analyze the EEG recorded before, during and after seizures from sixteen patients with pharmacoresistant focal-onset epilepsy. The data is filtered to low (4–30 Hz) and high (80–150 Hz) frequencies. We define the multivariate phase-locking measure and the univariate phase-locking contribution measure. Surrogate signals are used to estimate baseline results expected under the null hypothesis that the EEG is a correlated linear stochastic process. ResultsOn average, nodes from inside and outside the seizure onset zone (SOZ) increase and decrease, respectively, the large-scale phase-locking. This difference becomes most evident in a joint analysis of low and high frequencies. ConclusionsNodes inside and outside the SOZ play opposite roles for the large-scale phase-locking in functional EEG network in epilepsy patients. SignificanceThe application of the phase-locking contribution measure to EEG recordings from epilepsy patients can potentially help in localizing the SOZ.