Scale-free structures emerging from co-evolution of a network and the distribution of a diffusive resource on it

Synchronization transitions in Kuramoto networks with higher-mode interaction

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type.

A model for simulating emergent patterns of cities and roads on real-world landscapes

Emergence of cities and road networks have characterised human activity and movement over millennia. However, this anthropogenic infrastructure does not develop in isolation, but is deeply embedded in the natural landscape, which strongly influences the resultant spatial patterns. Nevertheless, the precise impact that landscape has on the location, size and connectivity of cities is a long-standing, unresolved problem. To address this issue, we incorporate high-resolution topographic maps into a Turing-like pattern forming system, in which local reinforcement rules result in co-evolving centres of population and transport networks. Using Italy as a case study, we show that the model constrained solely by topography results in an emergent spatial pattern that is consistent with Zipf’s Law and comparable to the census data. Thus, we infer the natural landscape may play a dominant role in establishing the baseline macro-scale population pattern, that is then modified by higher-level historical, socio-economic or cultural factors.

Generalized splay states in phase oscillator networks

Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass of phase-locked states with vanishing mth order parameter. Such states typically manifest incoherent dynamics, and they often create high-dimensional families of solutions (splay manifolds). For a general class of phase oscillator networks, we provide explicit linear stability conditions for splay states and exemplify our results with the well-known Kuramoto-Sakaguchi model. Importantly, our stability conditions are expressed in terms of just a few observables such as the order parameter or the trace of the Jacobian. As a result, these conditions are simple and applicable to networks of arbitrary size. We generalize our findings to phase oscillators with inertia and adaptively coupled phase oscillator models.

Model framework for emergence of synchronized oscillations

Autonomy is an important concept when investigating the mechanism whereby biological systems exhibit flexibility against unpredictable environmental changes. Herein we propose a parameter-tuning algorithm, based on a selection principle, that allows the emergence of synchronization between populations of oscillators through autonomous changes of the intrinsic parameters. With the algorithm, the populations exhibit self-recovery of the synchronized state after the existing synchronized state is broken suddenly; that is, the system chooses appropriate values of the intrinsic parameters to recover the synchronized state. We also propose a continuous model in which the selection is described by the replicator model and the parameter values are determined by the density profile of the oscillators in parameter space.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

The Role of Clustering in the Adoption of Organic Dairy: A Longitudinal Networks Analysis between 2002 and 2015

This paper uses network analysis to study the geo-localization decisions of new organic dairy farm operations in the USA between 2002 and 2015. Given a dataset of organic dairy certifications we simulated spatio-temporal networks based on the location of existing and new organic dairy farming operations. The simulations were performed with different probabilities of connecting with existing or incoming organic farmer operations, to overcome the lack of data describing actual connections between farmers. Calculated network statistics on the simulated networks included the average degree, average shortest path, closeness (centrality), clustering coefficients, and the relative size of the largest cluster, to demonstrate how the networks evolved over time. The findings revealed that new organic dairy operations cluster around existing ones, reflecting the role of networks in the conversion into organic production. The contributions of this paper are twofold. First, we contribute to the literature on clustering, information sharing, and market development in the agri-food industry by analyzing the potential implications of social networking in the development of a relatively new agriculture market. Second, we add to the literature on empirical social networks by using a new dataset with information on actors not previously studied analytically.

Self-organization of complex networks as a dynamical system

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

Hodge-Kodaira decomposition of evolving neural networks

Although it is very important to scrutinize recurrent structures of neural networks for elucidating brain functions, conventional methods often have difficulty in characterizing global loops within a network systematically. Here we applied the Hodge-Kodaira decomposition, a topological method, to an evolving neural network model in order to characterize its loop structure. By controlling a learning rule parametrically, we found that a model with an STDP-rule, which tends to form paths coincident with causal firing orders, had the most loops. Furthermore, by counting the number of global loops in the network, we detected the inhomogeneity inside the chaotic region, which is usually considered intractable.

Self-healing networks: redundancy and structure

We introduce the concept of self-healing in the field of complex networks modelling; in particular, self-healing capabilities are implemented through distributed communication protocols that exploit redundant links to recover the connectivity of the system. We then analyze the effect of the level of redundancy on the resilience to multiple failures; in particular, we measure the fraction of nodes still served for increasing levels of network damages. Finally, we study the effects of redundancy under different connectivity patterns—from planar grids, to small-world, up to scale-free networks—on healing performances. Small-world topologies show that introducing some long-range connections in planar grids greatly enhances the resilience to multiple failures with performances comparable to the case of the most resilient (and least realistic) scale-free structures. Obvious applications of self-healing are in the important field of infrastructural networks like gas, power, water, oil distribution systems.

Spatio-temporal dynamics in collective frog choruses examined by mathematical modeling and field observations

This paper reports theoretical and experimental studies on spatio-temporal dynamics in the choruses of male Japanese tree frogs. First, we theoretically model their calling times and positions as a system of coupled mobile oscillators. Numerical simulation of the model as well as calculation of the order parameters show that the spatio-temporal dynamics exhibits bistability between two-cluster antisynchronization and wavy antisynchronization, by assuming that the frogs are attracted to the edge of a simple circular breeding site. Second, we change the shape of the breeding site from the circle to rectangles including a straight line, and evaluate the stability of two-cluster and wavy antisynchronization. Numerical simulation shows that two-cluster antisynchronization is more frequently observed than wavy antisynchronization. Finally, we recorded frog choruses at an actual paddy field using our sound-imaging method. Analysis of the video demonstrated a consistent result with the aforementioned simulation: namely, two-cluster antisynchronization was more frequently realized.