اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدVerhulst-Lotka-Volterra (VLV) model of ideological struggles
59
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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
. It is shown that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical system and a graph-theoretic approach based on the Tree-Cycle identity.
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
eal social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks.
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
icality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent $alpha<2$, unlike preferential-attachment models), similar to those seen in empirical data.
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
rated in the model through a stochastic resetting dynamics of the predators to the prey patch. We solve in the long time limit the rate equations of Lotka-Volterra type that describe the evolution of the two species densities. Fixing the demographic parameters and the Levy exponent, the total population of predators can be maximized for a certain value of the resetting rate. This optimal value achieves a compromise between over-exploitation and under-utilization of the habitat. Similarly, at fixed resetting rate, there exists a Levy exponent which is optimal regarding predator abundance. These findings are supported by 2D stochastic simulations and show that the combined effects of diffusion and resetting can broadly extend the region of species coexistence in ecosystems facing resources scarcity.
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
xinmathbb{R} end{cases} quad (1) end{equation} where $d,r,a$, and $b$ are positive constants with $a eq 1$ and $b eq 1$. We prove the existence of some entire solutions $(u(t,x),v(t,x))$ of $(1)$ corresponding to $(Phi_{c}(xi),0)$ at $t=-infty$ (where $xi=x-ct$ and $Phi_c$ is a traveling wave solution of the scalar Fisher-KPP defined by the first equation of $(1)$ when $a=0$). Moreover, we also describe the asymptotic behavior of these entire solutions as $tto+infty$. We prove existence of new entire solutions for both the weak and strong competition case. In the weak competition case, we prove the existence of a class of entire solutions that forms a 4-dimensional manifold.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
