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Das K.P.,Mahadevananda Mahavidyalaya | Chattopadhyay J.,Indian Statistical Institute
Mathematical Methods in the Applied Sciences | Year: 2012

An eco-epidemiological model with random environmental disturbance is proposed and analyzed. We assume that the susceptible prey population can acquire infection both from external sources and from internal transmission of the disease. It is also assumed that there is no recovery of the disease, and the consumption of diseased prey has a deleterious effect on the predator population. The conditions for the extinction of the predator and the prey populations are worked out. The most important observation of the present investigation is that oscillatory behavior of the populations observed in deterministic framework undergoes stable coexistence in the stochastic framework. Copyright © 2012 John Wiley & Sons, Ltd. Source

Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95(3) (2009) 188-199] proposed an eco-epidemiological model where the prey species is infected through the external source of infection and contact of the species. In this present study we have modified their model by assuming that the predator consumes both the susceptible as well as the infected prey following the modified Holling type-II functional response. Our main focusing points of this study are the role of infection rate (both internal and external), alternative food, and half-saturation constant in the predator-prey dynamics with disease in the prey population. We have shown the local stability of the boundary as well as the interior equilibrium point under certain conditions. We have also worked out the permanence of the system. Our simulation results show that the system enters into limit cycle oscillations from stable position for higher values of the contact rate. But it is also shown that the external infection rate, enrichment of the alternative food of the predator population and the half-saturation constant can prevent limit cycle oscillations and stabilize the system. Thus external disease propagation, enrichment of the alternative food resource, and the half-saturation constant are the key factors for preventing the oscillatory behavior of the species. © 2015 World Scientific Publishing Company. Source

Das K.,Mahadevananda Mahavidyalaya
Journal of Dynamical and Control Systems | Year: 2015

The effect of parasites and pathogens in the prey population received a lot of attention, but disease in the predator population has been studied comparatively little in literature. In this study, we have considered a predator-prey model with disease in the predator population. Here, we have analyzed the local stability of the model system around the equilibria. We have derived the ecological as well as the disease basic reproduction numbers and analyzed the community structure of the model system by these numbers. Our numerical results reveal that disease introduction in the predator population produces chaotic dynamics. We have observed stable focus, limit cycles, period doubling, and chaos for variation of the force of infection in the predator population. It is also observed that half-saturation constants are responsible for occurrence and control of chaos. It is found that chaos may be prevented by increasing the predation efficiency of the infected predator. © 2015, Springer Science+Business Media New York. Source

Banik M.,Indian Statistical Institute | Gazi M.D.R.,Indian Statistical Institute | Das S.,se National Center For Basic Science | Rai A.,se National Center For Basic Science | Kunkri S.,Mahadevananda Mahavidyalaya
Journal of Physics A: Mathematical and Theoretical | Year: 2012

Bells theorem teaches us that there are quantum correlations that cannot be simulated by just shared randomness (local hidden variable). There are some recent results which simulate the singlet correlation by using either 1 bit or a binary (no-signaling) correlation which violates Bells inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, Hall showed that the statistics of a singlet state can be generated by sacrificing measurement independence where underlying distribution of hidden variables depends on measurement directions of both parties (Hall 2010 Phys. Rev. Lett. 105 250404). He also proved that for any model of singlet correlation, 86% measurement independence is optimal. In this paper, we show that 59% measurement independence is optimal for simulating the singlet correlation when the underlying distribution of hidden variables depends only on the measurements of one party. We also show that a distribution corresponding to this optimal lack of free will already exists in the literature which first appeared in the context of detection efficiency loophole (Gisin and Gisin 1999 Phys. Lett. A 3237). © 2012 IOP Publishing Ltd. Source

Gayen P.,Raja Peary Mohan College | Sarker K.K.,Mahadevananda Mahavidyalaya | Sinha C.,Jadavpur University
Colloids and Surfaces A: Physicochemical and Engineering Aspects | Year: 2013

Photochromism is dependent on the structure of material and matrix. 1-Alkyl-2-(arylazo)imidazole exists at ambient condition in trans-geometry about NN group. UV light irradiation in toluene solution of the compound has changed their trans structure to cis structure. These two isomers have different absorption spectra. The cis-to-trans isomerization proceeds slowly in visible light irradiation while it is appreciably fast with increasing temperature under thermal process. The rate of trans-to-cis isomerization is increased by 30-70% in presence of neutral (Triton-X-100) and cation (CTAB) micelle while anion micelle (SDS) reduces the same by 34-49%. The quantum yield of the photoisomerization is also increased by 33-84% in presence of neutral and cationic micelle. The activation energy (Ea) of cis→trans thermal isomerization is amplified in presence of Triton-X-100 and CTAB while it is decreased by adding SDS. Thus, the lowering of cis-to-trans thermal process in presence of neutral and cation micelle and increasing in SDS phase is justified. © 2013 Elsevier B.V. Source

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