A remark on "Study of a Leslie-Gower-type tritrophic population model" [Chaos, Solitons and Fractals 14 (2002) 1275-1293]

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.Comment: 10 pages, 4 figure

What is India speaking: The "Hinglish" invasion

While language competition models of diachronic language shift are increasingly sophisticated, drawing on sociolinguistic components like variable language prestige, distance from language centers and intermediate bilingual transitionary populations, in one significant way they fall short. They fail to consider contact-based outcomes resulting in mixed language practices, e.g. outcome scenarios such as creoles or unmarked code switching as an emergent communicative norm. On these lines something very interesting is uncovered in India, where traditionally there have been monolingual Hindi speakers and Hindi/English bilinguals, but virtually no monolingual English speakers. While the Indian census data reports a sharp increase in the proportion of Hindi/English bilinguals, we argue that the number of Hindi/English bilinguals in India is inaccurate, given a new class of urban individuals speaking a mixed lect of Hindi and English, popularly known as "Hinglish". Based on predator-prey, sociolinguistic theories, salient local ecological factors and the rural-urban divide in India, we propose a new mathematical model of interacting monolingual Hindi speakers, Hindi/English bilinguals and Hinglish speakers. The model yields globally asymptotic stable states of coexistence, as well as bilingual extinction. To validate our model, sociolinguistic data from different Indian classes are contrasted with census reports: We see that purported urban Hindi/English bilinguals are unable to maintain fluent Hindi speech and instead produce Hinglish, whereas rural speakers evidence monolingual Hindi. Thus we present evidence for the first time where an unrecognized mixed lect involving English but not "English", has possibly taken over a sizeable faction of a large global population.Comment: This paper has been withdrawan as the model has now been modified and the existing model has some error

Novel Dynamics in an Additional Food provided Predator-Prey System with mutual interference

The provision of additional food (AF) sources to an introduced predator has been identified as a mechanism to improve pest control. However, AF models with prey dependent functional responses can cause unbounded growth of the predator \cite{S27}. To avoid such dynamics, an AF model with mutual interference effect has been proposed \cite{S02}. The analysis therein reveals that if the quantity of additional food $\xi > h(\epsilon)$, where $\epsilon$ is the mutual interference parameter, then pest eradication is possible, and this is facilitated via a transcritical bifurcation. We revisit this model and show novel dynamical behaviors. In particular, pest eradication is possible for a tighter range of AF $g(\epsilon) < \xi < f(\epsilon) < h(\epsilon)$, and can also occur via a saddle node bifurcation. We observe bi-stability, as well as local bifurcations of Hopf type. We also prove a global bifurcation, of homoclinic type. This bifurcation in turn is shown to create a non-standard dynamic wherein the pest extinction state becomes an ``almost" global attractor. To the best of our knowledge, this is the first proof of existence of such a dynamical structure in AF models. We discuss our analysis in the context of designing novel bio-control strategies