Dr. Tapan Kumar Kar Dr. Tapan Kumar Kar Associate Professor, Mathematics PhD (Jadavpur University), Thesis title: Some Mathematical Models on Bioeconomic Harvesting Problems of Multispecies Fisheries. Supervisor: Professor Kripasindhu Chaudhuri, Jadavpur University. M.Phil (Calcutta University) Applied Mathematics, Specialization: Mathematical Ecology. GATE qualified, MHRD, Govt. of India. NET qualified (Joint CSIR-UGC) MSc.(Calcutta University) Applied Mathematics, Specialization: Mathematical Biology. BSc (Honours) (Calcutta University) Major: Mathematics, Minors: Physics and Chemistry. Contact Addresses Residence EE-103/1, Salt Lake, Sector-II, Kolkata-700091, West Bengal, India Phone (office) +91 - 33 - 26684561/62/63 Ext. 529 Mobile +91 - email t_k_kar@yahoo.com, tkar1117@gmail.com Research Areas Mathematical Ecology. Recent Publications Kar, T. K. and Chaudhuri, K. S., On non-selective harvesting of a multispecies fishery. Int. J. Math. Educ. Sci. Technol. 33(4)(2002)543-556 ( Taylor & Francis). Kar, T. K. and Chaudhuri, K. S., On non-selective harvesting of two competing fish species in the presence of toxicity, Ecological Modelling, 161(2003)125-137(Elsevier). Kar, T. K. and Chaudhuri K. S., Regulation of a prey-predator fishery by taxation: a dynamic reaction model. Journal of Biological System, 11 (2)(2003)173-187 ( World Scientific). Kar, T. K. and Chaudhuri, K. S., Regulation of a prey-predator fishery by taxation. Int. J. Math. Educ. Sci. Technol., .34(3)(2003)403-416 ( Taylor & Francis). Kar, T. K. , Selective harvesting in a prey-predator fishery with time delay. Math. Comp. Model. 38(2003) 449-458 (Elsevier). Kar, T. K. , Optimal harvesting and stability for a prey-predator system with stage structure, Advances in Modelling and Analysis Series D, 8(3)(2003) 61-71(AMSE periodicals, France). Kar, T. K. and Chaudhuri, K. S., Harvesting in a two prey one predator fishery: a bioeconomic model. The ANZIAM J. 45(3)(2004) 443-456 (Australian Mathematical Society). Kar, T. K. , A bioeconomic model of harvesting in a tritrophic food chain fishery, Int. J. Nonl. Model. Sci. Eng. 2(1)(2004) 1-12. Kar, T. K. Influence of environmental noises on the Gompertz model of two species fishery. Ecological Modelling, 173(2/3)(2004) 283-293 (Elsevier). Kar, T. K. Stability analysis of a prey-predator model with delay and harvesting. J. Biological Systems. 12(1)(2004)1-11(World Scientific). Kar, T. K. Conservation of a fishery through optimal taxation: a dynamic reaction model. Commu. Nonl. Sci. Num. Simul. 10(2)(2004) 121-131(Elsevier) Kar, T. K. and Chaudhuri, K. S. On selective harvesting of two competing fish species in the presence of environmental fluctuation. Natural Resource Modeling, 17(4)(2004)1-23( USA). Kar, T. K. Pahari, U.K. and Chaudhuri, K. S, Management of a single species fishery with stage structure. Int. J. Math. Edu. Sci. Tech. 35(3)(2004) 403-414 ( Taylor & Francis ). Kar, T. K. Management of a fishery based on continuous fishing effort. Nonlinear Analysis: Real World Application, 5/4(2004)629-644(Elsevier, USA). Kar, T. K. Pahari, U.K. and Chaudhuri, K. S., Management of a prey-predator fishery based on continuous fishing effort. J. Biol. Syst. 12(3)(2004)1-13( World Scientific, Canada). Kar, T. K., Optimal harvesting and stability in a three level food chain fishery. Advances in Modelling and Analysis Series D, 25(1)(2004)31-46(AMSE Periodicals, France). Kar, T. K. Stability of a stage structured prey-predator model. Advances in Modelling and Analysis Series D, 9(3)(2004)15-26 (AMSE Periodicals, France). Kar, T. K. Stability analysis of a prey-predator model incorporating a prey refuge. Communications in Nonlinear Sciences and Numerical Simulation 10(6)(2005)681-691(Elsevier). Kar, T. K., Pahari U. K. and Chaudhuri K. S., Conservation of a prey-predator fishery based on continuous fishing effort. Journal of Applied Mathematics and Computing, 19(1/2)(2005)311-326 (Korea). Kar, T. K., Stability and optimal harvesting of a prey-predator model with stage-structure for predator, Applicationes Mathematicae, 32(2005)279-291(Polland). Kar, T. K. and Pahari, U. K. Non-selective harvesting in prey-predator models with delay, Communications in Nonlinear Science and Numerical Simulation. 11(4)(2005)499-509 (Elsevier). Kar, T. K. Optimal harvesting and stability for a prey-predator system with stage-structure for predator, Advances in Modelling and Analysis, Series D, 10(1)(2005)53-62(AMSE Periodicals, France). Kar, T. K. Modelling and analysis of a harvested prey-predator system incorporating a prey refuge. Journal of Computational and Applied Mathematics, 185(2006)19-33 (Elsevier). Kar, T. K. and Matsuda H, Modelling and Analysis of Marine Reserve Creation, Journal of Fisheries and Aquatic Sciences. 1(1)(2006)17-32(Academic Journals Inc). Kar, T. K., A mathematical model on bioeconomic harvesting of a nonlinear prey-predator fishery, Int. J. Math. Educ. Sci. Technol., 37(3)(2006)309-319 (Taylor & Francis). Kar, T. K. and Matsuda H, Controllability of a harvested prey-predator system with time delay, Journal of Biological Systems, 14(2)(2006)1-12.(World Scientific). Kar, T. K., Controllability and optimal harvesting of a prey-predator model incorporating a prey refuge, Int. J. Math. Educ. Sci. Technl., 37(5) (2006) 559-571.(Taylor & Francis). Kar, T. K. and Misra Swarnakamal, Influence of prey reserve in a prey-predator fishery, Nonlinear Analysis 65 (2006)1725-1735 ( Elsevier). Kar, T. K., Misra Swarnakamal, Mukhopadhyay B., A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting, Journal of Applied Mathematics and Computing 22(2006)(1/2)387-401 (Korea ). Kar, T. K. and Matsuda H., An overview of bioeconomic analysis and management in fisheries, Journal of Fisheries and Aquatic Sciences 1(3)(2006)218-234(Academic Journals Inc, USA). Kar, T. K. and Misra Swarnakamal, Optimal control of a fishery under critical depensation. Journal of Fisheries and Aquatic Sciences 1(3)(2006)253-261 (Academic Journals Inc). Kar, T. K., Pahari U. K., Modelling and analysis of a prey-predator systems with stage-structure and harvesting, Nonlinear Analysis: Real World Applications 8(2007)601-609 (Elsevier). Kar, T. K. and Matsuda H., Global dynamics and controllability of a harvested prey-predator systems with Holling type III functional response. Nonlinear Analysis : Hybrid Systems:1(2007)59-67 (Elsevier). Kar, T. K., Pahari U. K., A model for prey-predator fishery with marine reserve, Journal of Fisheries and Aquatic Sciences 2(3)(2007)195-205 (Academic Journals Inc). Kar, T. K., Dynamics of a ratio-dependent prey-predator system with selective harvesting of predator species, Journal of Applied Mathematics and Computing 23(2007)(1/2)385-395(Korea). Kar, T. K., A model for fishery resource with reserve area and facing prey-predator interaction, Canadian Applied Mathematics Quarterly 14(4)(2006)387-401(Canada). Kar, T. K. and Matsuda H, Permanence and optimization of harvesting return: a stage structured prey-predator fishery, Research Journal of Environmental Sciences 1(2)(2007)35-46. Kar, T. K., Misra Swarnakamal, Modelling and analysis of a prey-predator system with stage-structure and harvesting, Advances in Modelling and Analysis, Series D, 12(3)(2007)31-44. Kar, T. K. and Matsuda H, Regulation of a multi-fleet fishery., Research Journal of Environmental Sciences 1(3)(2007)93-101(Academic Journal Inc). Kar, T. K. and Matsuda H, Sustainable management of a fishery with a strong Alee effect, Trends in Applied Science Research 2(4)(2007)271-283. Kar, T. K. and Matsuda H, A bioeconomic model of a single species fishery with marine reserve, Journal of Environmental Management 86(1)(2008)171-180 (Elsevier). Kar, T. K. and Batbyal Ashim. (2009): Stability and bifurcation of a prey-predator model with time delay, C. R. Biologies 332, 642-651 (Elsevier) Kar, T. K. and Chakraborty, K. (2009): Marine reserves and its consequences as a fisheries management tool. World Journal of Modelling and Simulation, 5(2), 83-95 (World Academic Press). Kar, T. K. and Chattopadhyay, S. K. A bioeconomic model of two-prey one predator system, Journal of Applied Mathematics and Informatics 27(5/6)(2009) 1411-1427. Kar, T. K. and Chattopadhyay, S. K. Bioeconomic modeling: an application to the North-East Atlantic cod fishery, Journal of Mathematics Research 1(2) (2009) 164-178 (CCSE, Canada). Kar, T. K. and Batabyal Ashim. Persistence and extinction of two prey and one predator system, Int. J. Engg. Sci. & Tech. 2(2) (2010) 174-190. Kar, T. K. and Chattopadhyay, S. K. and Agarwal, R. P., Dynamics of an exploited prey-predator system with non-monotonic functional response, Communications in Applied Analysis, 14(1)(2010)21-38 (USA). Kar, T. K. and Batbyal Ashim, Modeling and analysis of an epidemic model with non-monotonic incidence rate under treatment. J. Math. Res., 2(1) (2010)103-115. Kar, T. K. and Batabyal, Ashim. Optimal use of fertilizer to overcome the effects of toxicity in plants J. Math. Res., 2(1)(2010), 103-115 Kar, T. K. and Chakraborty, K. Bioeconomic analysis of fishery with reference to the optimal utilization and management of the resource: An application to the Marylandâ€™s Chesapeake Bay oyster fishery, Int. J. Engg. Sci. Tech 1(1)(2009)172-189. Kar, T. K. and Misra Swarnakamal, A resource based stage structured fishery model with selective harvesting of mature species, Appl. Appl. Math. 5(1)(2010)42-58 (USA). Kar, T. K. and Chakraborty, K. Effort dynamics in a prey-predator model with harvesting. Int. J. Inf. & Syst. Sci. 6(3)(2010) 318-332. Kar, T. K. and Chakraborty, K. A bioeconomic assessment of the Bangladesh srimp fishery World J. Modelling & Simulation, 7(1)(2011)58-59 (World Academic Press). Kar, T. K. and Chakraborty, K and Pahari, U. K. A prey-predator model with alternative prey: Mathematical model and analysis. Canadian Applied Mathematics Quarterly, 18(2)(2010) 137-168 Kar, T. K., Batabyal, Ashim and Agarwal, R. P. Modelling and analysis of an epidemic model with classical Kermack Mckendrick incidence rate under treatment, J. KSIAM 14 (2010), 1-16 Kar, T. K. and Chakraborty, K. Bio-economic modelling of a prey-predator system using differential algebraic equations, Int. J.Engg. Sci. Tech., 2(1) (2010) 13-34 Kar, T. K. and Misra Swarnakamal and Batanyal Ashim, An analysis for a two species predator-prey system with harvesting, Int .J. Advn Sci.Techn. 1(5)(2010)84-99. Kar, T. K. and Chattopadhyay, S.K., A dynamic reaction model of a prey-predator system with stage-structure for predator, Modern Applied Sciences, 4(5)(2010)183-195. Kar, T. K. and Ghosh, Bapan, Bifurcation and feedback control of a stage-structure exploited prey-predator system. Int .J. Engg. Sci. Tech.2(6) (2010)131-141 Kar, T. K. and Chattopadhyay, S.K; A focus on long-run sustainability of a harvested prey-predator system in the presence of atternative prey, C. R. Biologies 333 (2010) 841-849 (Elsevier). Kar, T. K. and Batabyal, Ashim, Stability and optimal control of an SIR epidemic model by vaccination, BioSystems 104(2011)127-135 (Elsevier). Chakraborty, K. Chakraborty, M and Kar, T. K. Optimal control of harvest and bifurcation of a prey-predator model with stage structure. Applied Mathematics and Computation 217(2011)8778-8792 (Elsevier). Kar, T. K. and Ghorai, Abhijit, Dynamic behaviour of a delayed predator-prey model with harvesting, Applied Mathematics and Computation 217(2011)9085-9104 (Elsevier). Kar, T. K. and Mondal, Prasanta Kumar, Global dynamics and bifurcation in delayed SIR epidemic model, Nonlinear Analysis : Real world Applications 12(2011)2058-2068 (Elsevier). Chakraborty, K. Chakraborty, M and Kar, T. K. Bifurcation and control of a bioeconomic model of prey-predator system with time delay, Nonlinear Analysis: Hybrid Systems 5(2011)613-625 (ELSEVIER). Kar, T. K. and Ghosh, Bapan, Dynamic analysis of a biological economic model of prey-predator system with alternative prey, International J. Ecological Economics and Statistics, 25(2)2012, 12-32. Kar, T. K. and Pahari, U.K. Bifurcation and feedback controll in an exploited prey-predator system with stage structure for prey, Journal of Applied Mathematics and Informatics, 29(2011)(5/6)1193-1204. Chakraborty, K. Chakraborty, M and Kar, T. K. Regulation of a prey-predator fishery incorporating prey refuge by taxation: A dynamic reaction model. J. Biological Systems 19(3)(2011)417-445 (World Scientific). Chakraborty, K. Das, Sanjoy and Kar, T. K. Optimal control of effort of a stage structured prey-predator fishery model with harvesting, Nonlinear Analysis: Real World Applications 12(2011)3452-3467(Elsevier). Kar, T. K. and Mondal Prasanta, A mathematical study on the dynamics of an eco-epidemiological model in the presence of delay, Applications and Applied Mathematics: An International Journal 7(1)(2012)300-333 (USA). Kar, T. K. and Ghorai, Abhijit and Batabyal, Ashim. Global dynamics and bifurcation of a tri-trophic food chain model. World J. Modelling and Simulations, 8(1)(2012)66-80 (World Academic Press). Kar, T. K. and Ghosh Bapan, Sustainability and Optimal control of an exploited prey predator system through provision Chakraborty, K, Jana, Soovoojeet and Kar, T. K, Global dynamics and bifurcation in a stage-structured prey-predator fishery model with harvesting, Applied Mathematics and Computation 218(2012)9271-9290(Elsevier). Kar, T. K. Ghorai, Abhijit and Jana, Soovoojeet. Dynamics of pest and its predator model with disease in the pest and optimal use of pesticide. Journal of Theoretical Biology 310(7)(2012)187-198 (Elsevier). Jana, S. and Kar T . K., The Optimal allocation of ocean space for the purposes of fishery and ecotourism management, Marine Science 2(5)(2012)85-93(Scientific and Academic Publishing). Chakraborty, K, and Kar, T. K, Economic perspective of marine reserves in fisheries: A bioeconomic model, Mathematical Biosciences 240(2012)212-222(Elsevier). Kar, T. K. and Mondal, Prasanta, Global dynamics of a tuberculosis epidemic model bifurcation and the influence of backward bifurcation, Journal of Mathematical Modelling and Algorithms 11(4)(2012)433-459 (Springer). Jana, S. Chakraborty, M. Chakraborty, K. and Kar, T. K. Global stability and bifurcation of time delayed prey-predator system incorporating prey refuge. Mathematics and Computers in Simulations 85(2012)57-77(Elsevier). Chakraborty, K, Jana, S. and Kar, T. K, Effort dynamics of a delay induced prey-predator system with reserve, Nonlinear Dynamics 70(2012)1805-1829 (Springer). Kar, T. K. and Mondal, Prasanta, Dynamical behaviour of a tuberculosis model with outcome of reinfection and optimal steering, Int. J. Ecol. Eco. Statistics 28(1)(2013)49-79. Kar, T. K. and Jana S., A theoretical study on mathematical modeling of an infectious disease with application of optimal control. BioSystems 111(2013)37-50 (Elsevier). Kar, T. K. Ghorai, A. and Jana S., Dynamic consequences of prey refuges in a two predator one prey system, Journal of Biological Systems (World Scientific). In Press. Kar, T. K. and Jana Soovoojeet, Stability and bifurcation analysis of a stage structured predator-prey model with time delay. Applied Mathematics and Computation 219(8)(2013)3779-3792 (Elsevier). Kar, T. K.Jana, Soovoojeet and Ghorai, Abhijit, Effect of isolation in an infectious disease, International Journal of Ecological Economics and Statistics 29(2)(2013)87-106 (CESER). Kar, T. K. and Ghosh, Bapan. Sustainability and economic consequences of creating marine protected area in multi-species multi-activity context. Journal of Theoretical Biology 318(2013)81-90(Elsevier). Jana, Soovoojeet and Kar, T. K., Modelling and analysis of a prey-predator system with disease in the prey, Chaos, Solitons and Fractals 47(2013)42-53 (Elsevier). Ghosh, Bapan and Kar, T. K. Maximum sustainable yield and species extinction in ecosystem: Some new results. Journal of Biological Physics 39(1) (2013)(Springer). Chakraborty, K. Haldar, S. and Kar, T. K. Ecological sustainability of an optimal control system incorporationg partial closure for the publications, Nonlinear Analysis Real World Applications (Elsevier). In Press. Kar, T. K. and Ghosh, Bapan, Impacts of maximum sustainable yield policy to prey-predator systems. Ecological Modelling 250(2013)134-142 (Elsevier). Pahari, U. K. and Kar, T. K. Conservation of a resource based fishery model through optimal taxation, Nonlinear Dynamics 71(3)(2013)(Springer). Chakraborty, K. Das, K. and Kar, T. K. Combined harvesting of a stage structured prey-predator model incorporate cannibalism in competitive environment, C. R. Biologies 336(2013)34-45 (Elsevier). Chakreborty, K, Halder, S and Kar, T. K. Global stability and bifurcation analysis of a delay induced prey-predator system with stage-structure. Nonlinear Dynamics (2013) (Springer) Kar, T. K. and Das Uttam, Singular induced bifurcation and control of a bioeconomic model of an exploited prey-predator system. Canadian Applied mathematics Quarterly, In Press. Kar, T. K. and Jana, Soovoojeet , Application of three controls optimally in a vector-borne disease - a mathematical study, Communications in Nonlinear Science and Numerical Simulation (Elsevier), In Press. Kar, T. K. and Das, Uttam, Regulation of an exploited prey predator system: A dynamic reaction model, International Journal of Ecological Economics and Statistics, In Press. Chakraborty, K. Chakraborty, M. and Kar T. K. A bioeconomic assessment of the European Hake fishery, Under review. Kar, T. K. and Jana Soovoojeet, Dynamics of an epidemic problem in deterministic and stochastic way. In review. Ghosh, Bapan and Kar, T. K., Sustainable use of ecosystem services: Jointly determined ecological thresholds and economic trade-offs. In review. Ghorai, A. and Kar, T. K. Biological control of a prey-predator system in the presence of a super predator. In review. Kar, T. K. Das, Uttam and Jana, Soovoojeet, Modelling and Analysis of a delayed stage-structure prey-predator system with nonmonotonic functional response. In review. Pahari, U. K. and Kar, T. K., Global dynamics of a tri-trophic food chain model, Under review. Mondal, P. K. and Kar, T. K., Optimal treatment control and bifurcation analysis of a tuberculosis model with effect of multiple re-infections. In review Jana, S. and Kar, T. K. Control of pests through optimal use of pesticide and provision of additional food to their predators. Under review. Kar, T. K. and Mondal, P. K.,Global dynamics of a water-borne disease model with multiple transmission pathways. In review. Ghosh, Bapan and Kar, T. K., Possible ecosystem impacts of applying maximum sustainable yield policy in food chain models, Under review. Ghosh, Bapan, Kar, T. K. and Paul Prosenjit. Impacts of species enrichment and MSY policy in three species food chain and food web models. In review. Mondal, Prasanta, Jana, Soovoojeet and Kar, T. K., Global dynamics of an SIS epidemic model in fuzzy environment. Under review. Courses Undertaken Department of Mathematics, BESU, Shibpur - 7111 03, INDIA