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- ItemDevelopment of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators(Woodbury, NY : American Institute of Physics, 2017) Papadopoulos, Lia; Kim, Jason Z.; Kurths, Jürgen; Bassett, Danielle S.Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule-which preserves connections between more outof- phase oscillators while rewiring connections between more in-phase oscillators-can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree-frequency and frequency-neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules.
- ItemPoisson approximation and connectivity in a scale-free random connection model([Madralin] : EMIS ELibEMS, 2021) Iyer, Srikanth K.; Jhawar, Sanjoy KrFor abstract see PDF
- ItemA vital link: Water and vegetation in the anthropocene(Chichester : John Wiley and Sons Ltd, 2013) Gerten, D.This paper argues that the interplay of water, carbon and vegetation dynamics fundamentally links some global trends in the current and conceivable future Anthropocene, such as cropland expansion, freshwater use, and climate change and its impacts. Based on a review of recent literature including geographically explicit simulation studies with the process-based LPJmL global biosphere model, it demonstrates that the connectivity of water and vegetation dynamics is vital for water security, food security and (terrestrial) ecosystem dynamics alike. The water limitation of net primary production of both natural and agricultural plants - already pronounced in many regions - is shown to increase in many places under projected climate change, though this development is partially offset by water-saving direct CO2 effects. Natural vegetation can to some degree adapt dynamically to higher water limitation, but agricultural crops usually require some form of active management to overcome it - among them irrigation, soil conservation and eventually shifts of cropland to areas that are less water-limited due to more favourable climatic conditions. While crucial to secure food production for a growing world population, such human interventions in water-vegetation systems have, as also shown, repercussions on the water cycle. Indeed, land use changes are shown to be the second-most important influence on the terrestrial water balance in recent times. Furthermore, climate change (warming and precipitation changes) will in many regions increase irrigation demand and decrease water availability, impeding rainfed and irrigated food production (if not CO2 effects counterbalance this impact - which is unlikely at least in poorly managed systems). Drawing from these exemplary investigations, some research perspectives on how to further improve our knowledge of human-water-vegetation interactions in the Anthropocene are outlined.
- ItemConnection times in large ad hoc mobile networks(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Döring, Hanna; Faraud, Gabriel; König, WolfgangWe study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently and identically distributed in a large domain, with a space-dependent population density of finite, positive order and with a fixed time horizon. Messages are instantly transmitted according to a relay principle, i.e., they are iteratedly forwarded from participant to participant over distances 2R, with 2R the communication radius, until they reach the recipient. In mathematical terms, this is a dynamic continuum percolation model. We consider the connection time of two sample participants, the amount of time over which these two are connected with each other. In the above thermodynamic limit, we find that the connectivity induced by the system can be described in terms of the counterplay of a local, random, and a global, deterministic mechanism, and we give a formula for the limiting behaviour. A prime example of the movement schemes that we consider is the well-known random waypoint model (RWP). Here we describe the decay rate, in the limit of large time horizons, of the probability that the portion of the connection time is less than the expectation.