Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSimple reaction-diffusion population model on scale-free networks
283
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations.
rate research
Read More
We present new empirical evidence, based on millions of interactions on Twitter, confirming that human contacts scale with population sizes. We integrate such observations into a reaction-diffusion metapopulation framework providing an analytical expression for the global invasion threshold of a contagion process. Remarkably, the scaling of human contacts is found to facilitate the spreading dynamics. Our results show that the scaling properties of human interactions can significantly affect dynamical processes mediated by human contacts such as the spread of diseases, and ideas.
We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes. This model can be used to understand the important dynamic characteristics of a stochastic epidemic spreading over very large complex networks, being informative about the state of groups. Aggregating nodes by groups, the state space becomes smaller than the individual-based approach at the cost of aggregation error, which is strongly bounded by the isoperimetric inequality. We also develop a mean-field approximation of this framework to further reduce the state-space size. Finally, we extend the GgroupEM to multilayer networks. Since the group-based framework is computationally less expensive and faster than an individual-based framework, then this framework is useful when the simulation time is important.
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree distribution. We use two different approaches: the deterministic mean-field approximation used by Barabasi and Albert (but taking into account the nodes of the starting network), and the probability distribution of the degree of each node, which considers the stochastic process. Numerical simulations show that the accuracy of the predictions of the mean-field approximation depend on the contribution of the dispersion in the final distribution. The results in terms of the probability distribution of the degree of each node are very accurate when compared to numerical simulations. The analysis of the standard deviation of the degree distribution allows us to assess the influence of the starting core when fitting the model to real data.
We analyse the dynamics of fishing vessels with different home ports in an area where these vessels, in choosing where to fish, are influenced by their own experience in the past and by their current observation of the locations of other vessels in the fleet. Empirical data from the boats near Ancona and Pescara shows stylized statistical properties that are reminiscent of Kirman and Follmers ant recruitment model, although with two ant colonies represented by the two ports. From the point of view of a fisherman, the two fishing areas are not equally attractive, and he tends to prefer the one closer to where he is based. This piece of evidence led us to extend the original ants model to a situation with two asymmetric zones and finite resources. We show that, in the mean-field regime, our model exhibits the same properties as the empirical data. We obtain a phase diagram that separates high and low herding regimes, but also fish population extinction. Our analysis has interesting policy implications for the ecology of fishing areas. It also suggests that herding behaviour here, just as in financial markets, will lead to significant fluctuations in the amount of fish landed, as the boat concentration on one area at a given point in time will diminish the overall catch, such loss not being compensated by the reproduction of fish in the other area. In other terms, individually rational behaviour will not lead to collectively optimal results.
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)sim C^{-delta}$. We find that for non-fractal scale-free networks $delta = 2$, and for fractal scale-free networks $delta = 2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at AS level (N=20566), where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
