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Abstract: In this paper, motivated by the thoughts and methods of the mixture of preferential and uniform attachments, we extend the Barabási–Albert (BA) model, and establish a network model with the power-law accelerating growth and the mixture of the two attachment mechanisms. In our model, the number of edges generated by each newly-introduced node is proportional to the power of () of time , i.e., . By virtue of the continuum approach, we have deduced the degree distribution of our model with the extended power-law form . When the number of edges generated by each new node is much greater than the value of , the degree distribution will converge to the power-law form . When is much less than the value of , the degree distribution will converge to the exponential-law form . By virtue of numerical simulations, we also discuss the dependence of the degree distribution on the model’s parameters (where is considered as a constant in the simulations). Finally, we investigate the possible application of our model in the spreading and evolution of epidemics in some real-world systems. [Copyright &y& Elsevier]

Abstract: In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations. For the stochastic model, we show that the system admits unique positive global solution starting from the positive initial value. Then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes. Finally, we show that the system has a stationary distribution under certain parametric restrictions. Numerical simulations are carried out to substantiate the analytical results. [Copyright &y& Elsevier]