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 Physics , 2006, DOI: 10.1088/1367-2630/8/12/308 Abstract: We consider a modification of the voter model in which a set of interacting elements (agents) can be in either of two equivalent states (A or B) or in a third additional mixed AB state. The model is motivated by studies of language competition dynamics, where the AB state is associated with bilingualism. We study the ordering process and associated interface and coarsening dynamics in regular lattices and small world networks. Agents in the AB state define the interfaces, changing the interfacial noise driven coarsening of the voter model to curvature driven coarsening. We argue that this change in the coarsening mechanism is generic for perturbations of the voter model dynamics. When interaction is through a small world network the AB agents restore coarsening, eliminating the metastable states of the voter model. The time to reach the absorbing state scales with system size as $\tau \sim \ln N$ to be compared with the result $\tau \sim N$ for the voter model in a small world network.
 Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.67132 Abstract: Understanding language competition and extinction is an interdisciplinary challenge, and math models provide a tool for interpreting linguistic census data and possibly predict the language shift trend at the population scale. In this study, new data from previously examined areas were modeled, specifically Catalan and Spanish in Catalonia, Spanish and English in Houston, Texas, Dutch and French in Brussels, Euskera and Spanish in Spain and French and English in Canada. Three mathematical models of the language competition have been validated. The first is the Abrams-Strogatz model, which treats populations as having two monolingual groups. The second is the Castelló model, which considers bilingual speakers. The third is the Mira model, which considers language competition when the two languages have high similarities. It was found that the some of the data matched Abrams-Strogatz original model, but some divergences could still be addressed. It was also found that the Mira model needs some improvement in how it treats the differences between languages.
 Physics , 2006, DOI: 10.1209/0295-5075/77/38002 Abstract: Religiosity is one of the most important sociological aspects of populations. All religions may evolve in their beliefs and adapt to the society developments. A religion is a social variable, like a language or wealth, to be studied like any other organizational parameter. Several questions can be raised, as considered in this study: e.g. (i) from a macroscopic'' point of view : How many religions exist at a given time? (ii) from a microscopic'' view point: How many adherents belong to one religion? Does the number of adherents increase or not, and how? No need to say that if quantitative answers and mathematical laws are found, agent based models can be imagined to describe such non-equilibrium processes. It is found that empirical laws can be deduced and related to preferential attachment processes, like on evolving network; we propose two different algorithmic models reproducing as well the data. Moreover, a population growth-death equation is shown to be a plausible modeling of evolution dynamics in a continuous time framework. Differences with language dynamic competition is emphasized.
 Quantitative Biology , 2005, DOI: 10.1016/j.physa.2005.10.055 Abstract: The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have not yet been understood. We present a model of HIV quasispecies competition, that describes the conditions of viral quasispecies coexistence under different immune system conditions. Our model incorporates both T and B cells responses, and we show that the role of B cells is important and additive to that of T cells. Simulations of coinfection (simultaneous infection) and superinfection (delayed secondary infection) scenarios in the early stages (days) and in the late stages of the infection (years) are in agreement with emerging molecular biology findings. The immune response induces a competition among similar phenotypes, leading to differentiation (quasi-speciation), escape dynamics and complex oscillations of viral strain abundance. We found that the quasispecies dynamics after superinfection or coinfection has time scales of several months and becomes even slower when the immune system response is weak. Our model represents a general framework to study the speed and distribution of HIV quasispecies during disease progression, vaccination and therapy.
 Quantitative Biology , 2014, DOI: 10.1103/PhysRevE.90.042149 Abstract: We develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic Susceptible-Infected-Susceptible (SIS) model. Here we extend previous results due to Parsons and Quince (2007), Parsons et al (2008) and Lin, Kim and Doering (2012). The second model, a two-strain generalization of the stochastic Susceptible-Infected-Recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of sub-population sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the sub-populations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
 Physics , 2008, DOI: 10.1016/j.physa.2008.09.034 Abstract: Competition between languages or cultural traits diffusing in the same geographical area is studied combining the language competition model of Abrams and Strogatz and a human dispersal model on an inhomogeneous substrate. Also, the effect of population growth is discussed. It is shown through numerical experiments that the final configuration of the surviving language can be strongly affected by geographical and historical factors. These factors are not related to the dynamics of culture transmission, but rather to initial population distributions as well as geographical boundaries and inhomogeneities, which modulate the diffusion process.
 Acta Electrotechnica et Informatica , 2011, DOI: 10.2478/v10198-011-0002-2 Abstract: The article deals with modeling of a system with hybrid dynamics and with two tools for modeling of such systems. For purpose of modeling we chose the system of coupled tanks. The tanks are situated in different heights and dynamics of the system changes in the moment when the liquid level in the second tank runs over the height of bottom of the first tank. That represents hybrid nature of this system. We chose two tools for simulation of hybrid systems - MPT toolbox and HYSDEL and we specifically aim on modeling of the system of coupled tanks by both these tools and on comparison of these tools. The tools are free however they do not work independently but as a part of the simulation language Matlab.
 Quantitative Biology , 2014, Abstract: Gray wolves were reintroduced to Yellowstone National Park (YNP) in 1995. The population initially flourished, but since 2003 the population has experience significant reductions due to factors that may include disease-induced mortality, illegal hunting, park control pro- grams, vehicle induced deaths and intra-species aggression. Despite facing similar conditions, and interference competition with the wolves, the coyote population at YNP has persisted. In this paper we introduce an epidemiological framework that incorporates natural, human-caused and disease-induced mortality as well as interference competition between two species of predators. The outcomes generated by this theoretical framework are used to explore the impact of competition and death-induced mechanisms on predators coexistence. It is the hope that these results on the competitive dynamics of carnivores in Yellowstone National Park will provide park management insights that result in policies that keep the reintroduction of wolves successful.
 Physics , 2005, DOI: 10.1016/j.physa.2005.02.038 Abstract: We use Monte Carlo simulations and assumptions from evolutionary game theory in order to study the evolution of words and the population dynamics of a system comprising two interacting species which initially speak two different languages. The species are characterized by their identity, vocabulary and have different initial fitness, i.e. reproduction capability. The questions we want to answer are: a. Will the different initial fitness lead to a permanent advantage? b. Will this advantage affect the vocabulary of the species or the population dynamics? c. How will the spatial distributions of the species be affected? Does the system exhibit pattern formation or segregation? We show that an initial fitness advantage, although is very quickly balanced, leads to better spatial arrangement and enhances survival probabilities of the species. In most cases the system will arrive at a final state where both languages coexist. However, in cases where one species greatly outnumbers the other in population and fitness, then only one species survives with its final language having a slightly richer vocabulary than its initial language. Thus, our results offer an explanation for the existence and origin of synonyms in all currently spoken languages.
 Physics , 2009, DOI: 10.1140/epjb/e2009-00284-2 Abstract: We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.
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