The Calcutta Technical School

Kolkata, India

The Calcutta Technical School

Kolkata, India
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Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,The Calcutta Technical School
Natural Resource Modeling | Year: 2013

To understand the impact of predation by different types of predators on the vole population dynamics, we formulate a three differential equation model describing the population dynamics of voles, the "specialist predator" and the "generalist predator." First we perform a local stability study of the different steady states of the basic model and deduce that the predation rates of the "specialist" as well as the "generalist" predator are the main parameters controlling the existence/extinction criteria of the concerned populations. Next we analyze the model from a thermodynamic perspective and study the thermodynamic stability of the different equilibria. Finally using stochastic driving forces, we incorporate the exogenous factor of environmental forcing and investigate the stochastic stability of the system. We compare the stability criteria of the different steady states under deterministic, thermodynamic and stochastic situations. The analysis reveals that when the "specialist" and the "generalist" predator are modeled separately, the system exhibits rich dynamics and the predation rates of both types of predators play a major role in controlling vole oscillation and/or stability. These findings are also seen to resemble closely with the observed behavior of voles in the natural setting. Numerical simulations are carried out to illustrate analytical findings. © 2012 Wiley Periodicals, Inc.


Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,The Calcutta Technical School
Nonlinear Analysis: Modelling and Control | Year: 2011

In the present study, we consider a nutrient-autotroph-herbivore ecosystem model where the herbivore species is assumed to have a commercial value. We use a Holling type-II harvest function to model density dependent herbivore harvesting. Stability criteria of the resulting model is investigated both from analytical and numerical viewpoints. The investigation revealed the existence of a number of threshold values of the harvest rate that have a remarkable influence on the system dynamics. Next we incorporate a noise term in the parameter representing harvest rate to model the phenomenon of poaching as random harvesting. The stochastic model is analyzed for exponential mean square stability and the resulting criteria in terms of harvest related parameters obtained. These parameter thresholds could be utilized to develop effective harvesting strategies and wildlife management policies which take into account the overall survival of the ecological populations. © Vilnius University, 2011.


Bhattacharyya R.,The Calcutta Technical School | Mukhopadhyay B.,Central Calcutta Polytechnic
Nonlinear Analysis: Hybrid Systems | Year: 2010

In the present work, a mathematical model of predator-prey ecological interaction with infected prey is investigated. A saturation incidence function is used to model the behavioral change of the susceptible individuals when their number increases or due to the crowding effect of the infected individuals [V. Capasso, G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci. 42 (1978) 41-61]. Stability criteria for the infection-free and the endemic equilibria are deduced in terms of system parameters. The basic model is then modified to incorporate a time delay, describing a latency period. Stability and bifurcation analysis of the resulting delay differential equation model is carried out and ranges of the delay inducing stability and as well as instability for the system are found. Finally, a stability analysis of the bifurcating solutions is performed and the criteria for subcritical and supercritical Hopf bifurcation derived. The existence of a delay interval that preserves the stability of periodic orbits is demonstrated. The analysis emphasizes the importance of differential predation and a latency period in controlling disease dynamics. © 2009 Elsevier Ltd. All rights reserved.


Roy M.,The Calcutta Technical School | Barman S.,University of Calcutta
Journal of Engineering and Applied Sciences | Year: 2013

The recent techniques of spectrum estimation are based on linear algebraic concepts of subspaces. In this study, the researchers have used noise subspace method for finding hidden periodicities in DNA. With the vast growth of genomic sequences, the demand to identify accurately the protein coding regions in DNA is increasingly rising. In the past, several techniques involving various cross-fields have come up, among which application of digital signal processing tools is of prime importance. It is known that coding segments have a 3-base periodicity while non-protein coding regions do not have this unique feature. One of the most important spectrum analysis technique based on the concept of subspace is the minimum norm method. The minimum norm estimator developed in this study shows sharp period-3 peaks in coding regions completely eliminating background noise. Comparison of proposed method with existing Sliding Discrete Fourier Transform (SDFT) method popularly known as periodogram has been drawn on several genes from various organisms showing that the proposed method has effective approach towards gene prediction. Resolution, quality factor, sensitivity, specificity, miss rate, wrong rate and computation time are used to establish superiority of minimum norm gene prediction method over existing method.


Bhattacharyya R.,The Calcutta Technical School | Bera A.,The Calcutta Technical School | Mukhopadhyay B.,Central Calcutta Polytechnic
Journal of Systems Science and Complexity | Year: 2010

This paper studies a three tier ecological food chain model consisting of nutrient, autotroph, and herbivore populations. Regeneration of nutrient from dead autotroph and herbivore biomass by decomposers present in the soil is included. The time required for maturation of the herbivore population is incorporated as a distributed time delay. Next, the authors introduce the time lag required for regeneration of nutrient from the dead herbivore as a discrete time delay. Stability and bifurcation behavior of the one- and two-delay models are carried out and a comparative study of the significance of these delays in controlling the system dynamics is performed. Numerical simulations are done to justify analytical resultsand bifurcation behavior of the one- and two-delay models are carried out and a comparative study of the significance of these delays in controlling the system dynamics is performed. Numerical simulations are done to justify analytical results. © 2010 Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg.


Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,The Calcutta Technical School
Mathematical Biosciences | Year: 2012

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics. © 2012 Elsevier Inc.


Bhattacharyya R.,The Calcutta Technical School | Mukhopadhyay B.,Central Calcutta Polytechnic
Natural Resource Modeling | Year: 2014

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile-insect-free boundary equilibrium, the crop-free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results. © 2013 Wiley Periodicals, Inc.

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