Foss Smidt (gliderbeef55)

It is the purpose of this paper to justify the use of modulation equations for pattern forming systems in the case of multiple Turing instabilities with critical wave numbers having a ratio 12 by proving approximation results, presenting attractivity results, and discussing the existence of modulating fronts.Identification of multiple influential spreaders on complex networks is of great significance, which can help us speed up information diffusion and prevent disease from spreading to some extent. The traditional top-k strategy to solve an influence maximization problem based on node centrality is unsuitable for selecting several spreaders simultaneously because of influence overlapping. Besides, other heuristic methods have a poor ability to keep the balance between efficiency and computing time. In this paper, an efficient method is proposed to identify the decentralized influential spreaders on networks by edge percolation under the Susceptible-Infected-Recovered (SIR) model. Thanks to the average size of the connected component where one node is located under the edge percolation equivalent to the final spread range of this node under the SIR model approximately, it inspires us to choose suitable spreaders maximize the spread of influence. The experimental results show that our method has high efficiency compared with other benchmark methods on three synthetic networks and six empirical networks, and it also requires less time and cost.Modern view of network resilience and epidemic spreading has been shaped by percolation tools from statistical physics, where nodes and edges are removed or immunized randomly from a large-scale network. In this paper, we produce a theoretical framework for studying targeted immunization in networks, where only n nodes can be observed at a time with the most connected one among them being immunized and the immunity it has acquired may be lost subject to a decay probability ρ. We examine analytically the percolation properties as well as scaling laws, which uncover distinctive characters for Erdős-Rényi and power-law networks in the two dimensions of n and ρ. Taurine We study both the case of a fixed immunity loss rate as well as an asymptotic total loss scenario, paving the way to further understand temporary immunity in complex percolation processes with limited knowledge.In ecology, the intra- and inter-specific competition between individuals of mobile species for shared resources is mostly non-local; i.e., competition at any spatial position will not only be dependent on population at that position, but also on population in neighboring regions. Therefore, models that assume competition to be restricted to the individuals at that position only are actually oversimplifying a crucial physical process. For the past three decades, researchers have established the necessity of considering spatial non-locality while modeling ecological systems. Despite this ecological importance, studies incorporating this non-local nature of resource competition in an aquatic ecosystem are surprisingly scarce. To this end, the celebrated Scheffer's tri-trophic minimal model has been considered here as a base model due to its efficacy in describing the pelagic ecosystem with least complexity. It is modified into an integro-reaction-diffusion system to include the effect of non-local competition by introducing a weighted spatial average with a suitable influence function. A detailed analysis shows that the non-locality may have a destabilizing effect on underlying nutrient-plankton-fish dynamics. A local system in a stable equilibrium state can lose its stability through spatial Hopf and Turing bifurcations when strength of a non-local interaction is strong enough, which eventually generates a large range of spatial patterns. The relationship between a non-local interaction and fish predation has been established, which shows that fish predation contributes in damping of plankton oscillations. Overall, re