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Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds of influences can be used, in such a model, for describing the dynamics of an agent opinion conversion: this can occur (i) either by means of mass communication tools, under some external field influence, or (ii) by means of direct interactions between agents. It results, among other features, that change(s) in environmental conditions can prevent the extinction of populations of followers of some ideology due to different kinds of resurrection effects. The tension arising in the country population is proposed to be measured by an appropriately defined scale index.
The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and cycle-balanced
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of r
Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at crit
We study the dynamics of predator-prey systems where prey are confined to a single region of space and where predators move randomly according to a power-law (Levy) dispersal kernel. Site fidelity, an important feature of animal behaviour, is incorpo
This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system begin{equation}label{eq:abstract} begin{cases} u_{t}= u_{xx} + u(1-u-av), & qquad xinmathbb{R} cr v_{t}= d v_{xx}+ rv(1-v-bu), & qquad