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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.

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.

Sarkar K.,Jadavpur University | Gayen V.,Central Calcutta Polytechnic
2014 2nd International Conference on Business and Information Management, ICBIM 2014 | Year: 2014

Noun phrase (NP) chunking deals with extracting the noun phrases from a sentence. While NP chunking is much simpler than parsing, it is still a challenging task to build an accurate and efficient NP chunker. Noun phrase chunking is an important and useful task in many natural language processing applications. It is studied well for English, however not much work has been done for Bengali. This paper presents a Bengali noun phrase chunking approach based on conditional random fields (CRFs) models. Our developed NP chunker has been tested on the ICON 2013 dataset and achieves an impressive F-score of 95.92. © 2014 IEEE.

Palit M.,Central Calcutta Polytechnic | Tudu B.,Jadavpur University | Bhattacharyya N.,Center for Development of Advanced Computing of India | Dutta A.,Jadavpur University | And 4 more authors.
Analytica Chimica Acta | Year: 2010

In an electronic tongue, preprocessing on raw data precedes pattern analysis and choice of the appropriate preprocessing technique is crucial for the performance of the pattern classifier. While attempting to classify different grades of black tea using a voltammetric electronic tongue, different preprocessing techniques have been explored and a comparison of their performances is presented in this paper. The preprocessing techniques are compared first by a quantitative measurement of separability followed by principle component analysis; and then two different supervised pattern recognition models based on neural networks are used to evaluate the performance of the preprocessing techniques. © 2010 Elsevier B.V.

Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,Calcutta Technical School
Applications of Mathematics | Year: 2010

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.

Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,Calcutta Technical School
Journal of Biological Systems | Year: 2011

In the present paper, we study a Prey-Predator-Pathogen model where the prey population suffer from an SI epidemic. The predator is assumed to exercise preferential predation. The prey preference mechanism ranges from predation only on the susceptible or only on the infective to proportional predation on both the prey types. The formulation maintains the native Holling type-II functional response in one hand and invokes prey switching on the other. We first describe stability and persistence results for the model without preference, which highlights the significance of some system parameters namely, predator mortality rate and predation pressure on the susceptible in shaping the system dynamics. Then we investigate the model with the preference mechanism, which shows the importance of the preference parameter (α) in controlling the stability and existence criteria of component populations. Our study reveals the existence of preference parameter ranges that (i) guarantees stable species coexistence (ii) exhibits rich dynamics in the form of oscillatory phenomena, point attractors and limit cycle attractors and (iii) causes possible extinction of the predators together with the susceptible prey. The ecological meaning of the corresponding ranges is also elaborated. © 2011 World Scientific Publishing Company.

Bhattacharyya R.,Calcutta Technical School | Mukhopadhyay B.,Central Calcutta Polytechnic
Nonlinear Analysis: Real World Applications | Year: 2010

In this paper, we study an eco-epidemiological model where prey disease is modeled by a Susceptible-Infected (SI) scheme. Saturation incidence kinetics is used to model the contact process. The predator population adapt switching technique among susceptible and infected prey. The prey species is supposed to be commercially viable and undergo constant non-selective harvesting. We study the stability aspects of the basic and the switching models around the infection-free state and the infected steady state from a local as well as a global perspective. Our aim is to study the role of harvesting and switching on the dynamics of disease propagation and/or eradication. A comparison of the local and global dynamical behavior in terms of important system parameters is obtained. Numerical simulations are done to illustrate the analytical results. © 2009 Elsevier Ltd. All rights reserved.

Mukhopadhyay B.,Central Calcutta Polytechnic | Bhattacharyya R.,Calcutta Technical School
Nonlinear Analysis: Real World Applications | Year: 2011

Stage-structured predatorprey models exhibit rich and interesting dynamics compared to homogeneous population models. The objective of this paper is to study the bifurcation behavior of stage-structured preypredator models that admit stage-restricted predation. It is shown that the model with juvenile-only predation exhibits Hopf bifurcation with the growth rate of the adult prey as the bifurcation parameter; also, depending on parameter values, a stable limit cycle will emerge, that is, the bifurcation will be of supercritical nature. On the other hand, the analysis of the model with adult-stage predation shows that the system admits a fold-Hopf bifurcation with the adult growth rate and the predator mortality rate as the two bifurcation parameters. We also demonstrate the existence of a unique limit cycle arising from this codimension-2 bifurcation. These results reveal far richer dynamics compared to models without stage-structure. Numerical simulations are done to support analytical results. © 2011 Elsevier Ltd. All rights reserved.

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