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Publications in International Journals
  1. Sajan, Choudhary Kapil Kumar and Dubey Balram, A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton system, Applied Mathematics and Compurtation, 458: 128236, 2023.
  2. Kumar Arjun, Gupta Ashvini, Dubey Uma S. and Dubey Balram, Stability and bifurcation analysis of an infectious disease model with different optimal control strategies, Mathematics and Computers in Simulation,213: 78-114, 2023.
  3. Pal Soumitra, Gupta Ashvini, Misra Arvind Kumar and Dubey Balram, Chaotic dynamics of a stage-structured prey-predator system with hunting cooperation and fear in the presence of two discrete delays, Journal of Biological Systems, 31(2): 611-642, 2023.
  4. Bhargava Masoom, Sajan, Dubey Balram, Trade-off and chaotic dynamics of prey–predator system with two discrete delays, Chaos 33, 053120, 2023. 
  5. Anshu, Dubey Balram, Sasmal Sourav Kumar and Sudarshan Anand, Consequences of fear effect and prey refuge on the Turing patterns in a delayed predator-prey system, Chaos 32, 123132, 2022.
  6. Gupta Ashvini and Dubey Balram, Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration, Chaos, Solitons and Fractals, 165: 112785, 2022.
  7. Gupta Ashvini, Kumar Ankit and Dubey B., Complex dynamics of Leslie-Gower prey-predator model with fear, refuge and additional food under multiple delays, Int. J. Biomath., 15(8): 2250060, 2022.
  8. Sajan, Dubey B. and Sasmak S.K., Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay, Chaos Solitons and Fractals, 160: 112245, 2022. https://doi.org/10.1016/j.chaos.2022.112245
  9. Sasmal S.K., Anshu and Dubey B., Diffusive patterns in a predator–prey system with fear and hunting cooperation, Eur. Phys. J. Plus 137: 281, 2022. htttps://doi.org/10.1140/epjp/s13360-022-02497-x
  10. Sajan, Sasmal S. K. and Dubey B., A phytoplankton-zooplankton-fish model with chaos control: In the presence of fear effect and an additional food, Chaos 32: 013114, 2022. https://doi.org/10.1063/5.0069474 
  11. Gupta Ashvini and Dubey B., Bifurcations and multi-stability in an eco-epidemic model with additional food, Eur. Phys. J. Plus 137:118, 2022. https://doi.org/10.1140/epjp/s13360-022-02340-3
  12. Sajan and Dubey B., Chaos control in a multiple delayed phytoplankton-zooplankton model with group defence and predator's interference, Chaos 31, 083101: 2021; doi: 10.1063/5.0054261
  13. Dubey P., Dubey Uma S. and Dubey B., Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response, Nonlinear Analysis: Modelling and Control, 26(4): 678-701, 2021. 
  14. Dubey B., Sajan and Kumar Ankit, Stability switching and chaos in a multiple delayed prey-predator model with fear effect and anti-predator behaviour, Mathematics and Computers in Simulation, 188: 164-192, 2021. 
  15. Kumar Ankit and Dubey B., Stability and Bifurcation of a prey-predator system with additional food and two discrete delays, Computer Modeling in Engineering & Sciences, 126 (2): 505-547, 2021. 
  16. Kumar Ankit and Dubey B., Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay, Nonlinear Analysis: Modelling and Control, 25(3): 417-442, 2020.
  17. Kumar Ankit and Dubey B., Modelling the effect of fear in a prey-predator system with prey refuge and gestation delay, International Journal of Bifurcation and Chaos, 29(14), 1950195 (25 pages), 2019.
  18. Dubey B. and Kumar Ankit, Dynamics of prey-predator model with stage structure in prey    including maturation and gestation delays, Nonlinear Dynamics, 96(4): 2653-2679, 2019.  
  19. Maiti A.P., Dubey B. and Charaborty A., Global analysis of a delayed stage structure prey-predator model with Crowley-Martin type functional response, Mathematics and computers in Simulation, 162: 58-84, 2019.  
  20. Dubey B., Kumar Ankit and Maiti A. P., Global stability and Hopf-bifurcation of prey-predator system with two discrete delays including habitat complexity and prey refuge, Comm. Nonlin. Sci. Numer. Simul., 67: 528-554, 2019..
  21. Dubey, B., Agarwal S, and Kumar Ankit, Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator, Nonlinear Analysis: Modelling and Control, 23(4): 493-514, 2018. 
  22. Dubey Preeti, Dubey Uma S. and Dubey B., Modeling the Role of Acquired Immune Response and Antiretroviral Therapy in the Dynamics of HIV Infection, Mathematics and Computers in Simulation, 144:12—137, 2018.
  23. Maiti A. P. and Dubey B, Stability and bifurcation of a fishery model with Crowley-Martin type functional response, International Journal of Bifurcation and Chaos, 27 (11), 1750174 (26pages), 2017. 
  24. Patra A.P., Dubey B. and Tushar Jai. A delayed prey-predator model with Crowley-Martin type functional response including prey refuge, Math. Meth. Appl. Sci., 40: 5792-5809, 2017.
  25. Thakur N.K., Tiwari S.K., Dubey B. and Upadhyay R.K., Diffusive three species plankton model in the presence of toxic prey: application to Sundarban mangrove wetland, J. Biol. Systems, 25(2): 185-206, 2017.
  26. Patra Atasi, Tushar Jai and Dubey B., Modeling and simulation of a wetland park: An application to Keoladeo National Park, India, Mathematics and Computers in Simulation, 134: 54-78, 2017.
  27. Lata K., Misra A. K. and Dubey B., Modeling the effects of wood and non-wood based industries on forestry resources, Natural Resource Modelling, 29(4): 559-580, 2016.
  28. Dubey B, Dubey Preeti and Dubey Uma S., Modeling the intracellular pathogen-immune interaction with cure rate, Comm. Nonlin. Anal. Numer. Simul., 38:72-90, 2016.
  29. Deka B.D., Patra Atasi, Tushar Jai and Dubey B., Stability and Hopf-bifu1ation in a general Gauss type two-prey and one-predator system, Appl. Math. Model., 40:5793-5818, 2016. http://dx.doi.org/10.1016/j.apm.2016.01.018 
  30. Dubey B., Dubey Preeti and Dubey Uma S., Role of media and treatment on an SIR model, Nonlinear Analysis: Modelling and Control, 21(2): 185-200, 2016.
  31. Dubey B., Dubey Preeti and Dubey Uma S., Dynamics of an SIR Model with nonlinear incidence and treatment rate, Appl. Appl. Math., 10(2):718-737, 2015.
  32. Dubey B., Hussain J., Raw S.N. and Upadhyay R. K., Modeling the effect of pollution on biological species: A socio-ecological problem, Computational Ecology and Software, 5(2): 152-174, 2015.
  33.  Dubey B., Patra Atasi and Sahani S. K., Modelling the dynamics of a renewable resource under harvesting with taxation as a control variable, Appl. Appl. Math., 9(2): 592-621, 2014.
  34. Upadhaya R.K., Patra A., Dubey B. and Thakur N.K., A predator-prey interaction model with self and cross diffusion in aquatic systems, J. Biol. Systems, Vol. 22, No. 4 (2014), 1450028, 22 pages, DOI: 10.1142/S0218339014500284.
  35. Dubey B., Patra A. and Upadhyay R.K., Dynamics of phytoplankton, zooplankton and fishery resource model, Appl. Appl. Math., 9(1), 217-245, 2014.
  36. Dubey B., Patra A., Srivastava P.K. and Dubey Uma S., Modeling and analysis of an SEIR model with different types of nonlinear treatment rates, J. Biol. Systems, Vol. 21, No. 3 (2013) 1350023, 25 pages, DOI: 10.1142/S021833901350023X 
  37. Upadhyay R. K.,  Naji R. K., Raw S. N., and  Dubey B., The role of top predator interference on the dynamics of a food chain model, Communications in Nonlinear Science and Numerical Simulation, 18(3), 757 – 768, 2013.
  38. Dubey B, and Patra Atasi, A mathematical model for optimal management and utilization of a renewable resource by  population, Journal of Mathematics, Vol 2013, Article ID 613706, 9 pages, 2013. 
  39. Dubey B, and Patra Atasi, Optimal Management of a Renewable Resource Utilized by a Population with Taxation as a Control Variable, Nonlinear Analysis: Modelling and Control, 18(1), 37-52, 2013.
  40. Dubey B., Modelling effects of two interacting populations on a renewable resource, Natural Resource Modeling, 25(2), 325 – 363, 2012. DOI: 10.1111/j.1939-7445.2011.00109. 
  41. Dubey B., Dubey Uma S. and Hussain J., Modelling effects of toxicant on uninfected cells, infected cells and immune response in the presence of virus, J. Biol. Systems, 19(3): 479-503, 2011.  DOI: 10.1142/S0218339011004081 
  42. Dubey B., Zhao T.G., Jonsson M.  and Rahmanov  H., A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using Boubaker polynomial expansion scheme, J. Theor. Biol., 264(1): 154 – 160, 2010.  (http://doi:10.1016/j.jtbi.2010.01.026).   
  43. Dubey B., Shukla J.B., Sharma S., Agarwal A. K. and  Sinha P. , A mathematical model  for chemical defense mechanism of two competing species,  Nonlinear Analysis : Real World Applications, 11: 1143 – 1158, 2010.  
  44. Upadhyay R.K., Thakur N.K. and Dubey B., Nonlinear non-equilibrium pattern formation in a spatial aquatic system: effect of fish predation, J. Biol. Systems, 18(1) : 129 – 159, 2010.    
  45. Misra A.K. and Dubey B., A ratio-dependent predator prey model with delay and harvesting, J. Biol . Systems, 18(2): 437 – 453. 2010.  
  46. Dubey B. and Narayanan A. S., Modelling effects of industrialization, population and pollution on a renewable resource, Nonlinear Analysis : Real World Applications, 11: 2853 – 2848, 2010.                                           (http://dx.doi.org/10.1016/j.nonrwa.2009.10.007 ).     
  47. Dubey B., A model for the effect of pollutant on human population dependent on a resource with environmental and health policy, J. Biol. Systems, 18(3): 571-592, 2010. DOI: 10.1142/S0218339010003378    
  48. Dubey B., Sharma S. Sinha P. and Shukla J.B., Modelling the depletion of forestry resources by population and population pressure augmented industrialization, Appl. Math. Model., 13 :  3002-3014, 2009.  
  49. Dubey B, Kumari Nitu, and Upadhyay R.K., Spatiotemporal Pattern formation in a Diffusive Predator-prey system: An analytical approach, J. Appl. Math. Comp., 31: 413 – 432, 2009.  
  50. Shukla J. B., Sharma S, Dubey B., and Sinha P., Modeling the survival of a resource dependent population: effects of toxicants (pollutants) emitted from external sources as well as formed by its precursors. Nonlinear Analysis : Real World Applications, 10 : 54-70, 2009.  
  51. Dubey B.,  Dubey Uma S. and Banerjee S., Modelling the interaction between avascular cancerous cells and acquired immune response. J. Biol. Systems,   16(3) : 337 – 356, 2008.  
  52. Dubey Uma S. and Dubey B., A mathematical model for the effect of toxicant on the immune system, J. Biol. Systems, 15(4) : 473 – 493, 2007.  
  53. Dubey B., A prey-predator model with a reserve area, Nonlinear Analysis : Modelling and Control, 12(4) : 479 -  494, 2007.  
  54. Dubey B. and Hussain J., Modelling the survival of species dependent on a  resource in a polluted environment. Nonlinear Analysis : Real – world Applications, 7 : 187 – 210, 2006.  
  55. Dubey B., A nonlinear model for the topsoil erosion caused by heavy rain, Nonlinear Analysis : Modelling and Control, 10(1) : 35 – 56, 2005.   
  56. Dubey B., Models for the effect of high speed wind on the depletion of fertile topsoil. Nat. Res. Model. 17(3): 229 – 249, 2004.   
  57. Dubey, B., A model for the effect of time delay on the dynamics of a population living in a polluted environment. J. Biol. Systems, 12(1): 35 – 43, 2004.  
  58. Dubey B. and Hussain J., Models for the effect of environmental pollution on forestry resources with time delay. Nonlinear Analysis : Real – world Applications, 5: 549 – 570, 2004.   
  59. Dubey B. and Upadhyay R.K., Persistence and extinction of one-prey and two predators system. Nonlinear Analysis : Modelling and Control, 9(4): 1 – 23, 2004.    
  60. Dubey  B and Hussain J., Nonlinear models for the survival of two competing species dependent on resource in industrial environments, Nonlinear Analysis: Theory, Method & Applications (Series B: Real-world Applications),4: 21 –   44,  2003.   
  61. Shukla J.B., Agarwal A.K., Sinha P. and Dubey B., Modelling effects of primary and secondary toxicants on renewable resources, Natural Resource Modelling, 16(1): 99 - 120, 2003.   
  62. Dubey B., Chandra, P. and Sinha P. ,  A model for inshore-offshore fishery, J. Biol. Systems, 11(1): 27-42, 2003. 
  63. Dubey B., Chandra, P. and Sinha P. , A model for fishery resource with reserve area. Nonlinear Analysis Real-world Applications, 4(4): 625 – 637,  2003.  
  64. Dubey, B., Dynamics of interacting biological species, Comments on Theoretical Biology, 8: 189 – 206, 2003.   
  65. Dubey B., Upadhaya, R.K. and Hussain, J., Effects of industrialization and pollution on resource biomass: a mathematical model. Ecol Model. 167: 83-95, 2003.   
  66. Dubey B., Chandra P. and Sinha P., A resource dependent fishery model with optimal harvesting policy, J. Biol. Systems, 10(1) 1-13, 2002.     
  67. Dubey B., Das B. and Hussain J., A predator-prey interaction model with self and cross-diffusion. Ecol. Model., 141(1-3): 67-76, 2001.   
  68. Shukla J. B., Agrawal A. K., Dubey B. and Sinha P., Existence and survival of two competing species in a polluted environment: a  mathematical model, J. Biological Systems, 9(2): 89-103, 2001.    
  69. Dubey B and Hussain J., Modelling the interaction of two biological species in a polluted environment, J. Math. Anal. Appl., 241(1):  58-79, 2000.    
  70. Dubey B. and Hussain J., A model for allelopathic effect on two competing  species, Ecol. Model., 129:    195-207, 2000.  
  71. Dubey B. and Das B., Models for the survival of species dependent on resource in industrial environments, J. Math. Anal. Appl., 231: 374-396, 1999.
  72. The water buffalo controversy in Keoladeo National Park, India-Reply, Ecol. Model., 106(1): 95-98, 1998.
  73. Dubey B., Modelling the depletion of forestry resources: Effects of two interacting populations, Ecol. Model., 101: 123-136, 1997.
  74. Shukla J. B. and Dubey B., Modelling the depletion and conservation of forestry resource: Effects of population and pollution, J. Math Biol., 36: 71-94, 1997.
  75. Shukla J. B. and Dubey B., Effect of changing habitat on species: Application to Keoladeo National Park, India, Ecol. Model.,  86:  91-99, 1996.
  76. Shukla A., Dubey B. and Shukla J. B., Effect of environmentally degraded soil on crop yield: The role of conservation, Ecol. Model., 86: 235-240, 1996.
  77.  Shukla J. B. and Dubey B., Simultaneous effect of two toxicants on biological species: A mathematical model, J. Biol. Syst., 4(1): 91-99, 1996.
  78. Shukla J. B., Dubey B. and Freedman H. I., Effect of changing habitat on survival of species, Ecol. Model., 87(1-3): 205-216, 1996.  
     Publications in National Journals
    1.      Dubey B., Das B. and Hussain J., A model for two competing species with self and cross-diffusion, Ind. J. Pure & Appl. Math., 33(6): 847-860, 2002. 
    2.        Dubey B. and Das B., Modelling the interaction of two predators competing for a prey in a diffusive system, Ind. J. Pure & Appl. Math., 31(7): 823-837, 2000.
    3.      Dubey B., Depletion and subsequent conservation of forestry resource biomass: a mathematical model, Proc. Nat. Acad. Sci., India, 68(A) IV: 373-386, 1998.
    4.        Dubey B., A resource based competition model: Effect of population, Far East J. Appl. Math., 1(1): 11-32, 1997.
    5.     Dubey B., Modelling the effect of toxicant on forestry resources, Ind. J. Pure and Appl.Math., 28(1): 1-12, 1997.
    6.      Dubey B. and Das B., Models for the migrating populations in a forested grassland, Far East J. Appl. Math., 1(1): 97-104, 1997. 
    7.     Dubey B., Time delay model for degradation of forestry resources, Ind. J. Ecol., 24 (1): 10-16, 1997.

       

       

      Publications in the Proceedings of International Conferences  

    1.      Gupta, A., Dubey, B. (2022). Bifurcation Analysis of a Leslie-Gower Prey-Predator Model with Fear and Cooperative Hunting. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity.  P. 1069–1080. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_90
    2.    Anshu, Sasmal, S.K., Dubey, B. (2022). Impact of Cooperative Hunting and Fear-Induced in a Prey-Predator System with Crowley-Martin Functional Response. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. pp 1015–1026. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_86
    3. 3. Sajan, Kumar, A., Dubey, B. (2022). Stability Switching in a Cooperative Prey-Predator Model with Transcritical and Hopf-bifurcations. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. pp 987–1000. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_84
    4.     Dubey P., Dubey B. and Dubey Uma S., Optimal control for therapeutic drug treatment on a delayed model incorporating immune response, Proceedings of the International Symposium on Mathematical and Computational Biology, BIOMAT 2015 (Edited by Rubem P Mondaini, Brazil), World scientific, pp. 221-240, June 2016. DOI: http://dx.doi.org/10.1142/9789813141919_0015 
    5.        Dubey P., Dubey B. and Dubey Uma S., An SIR model with nonlinear incidence rate and Holling type III treatment Rate, (Eds.:Cushing, J.M., Saleem, M., Srivastava , H.M., Khan, M.A., Merajuddin, M.), Springer Proceedings in Mathematics and Statistics: Applied Analysis in Biological and Physical Sciences, pp. 63-81, 2016. 
    6.       Dubey B. and Upadhyay R. K., A model for the effect of predation on two competing prey species, Mathematical Biology – Recent Trends (Eds. Peeyush Chandra and B. V. Rathish Kumar),  pp. 242 – 250, 2006.
    7.      Dubey B. and Hussain J., Time delay model for the depletion of forestry resources, Proc. International Conference on Mathematical Modelling, University of Roorkee, India,  616-620, 2001.
    8.    Shukla J. B., Agrwal A. K. and Dubey B., Effects of toxicants (pollutants) on biological species: some mathematical models. In Environmental Stress: Indication, Mitigation and Eco-conservation, M. Yunus, N. Singh and L. J. de Kok (Eds.), 345-356, Kluwer Academics, The Netherlands, 2000.
    9.      Dubey B., Mathematical Models for fishery resources in a polluted marine environment, Proc. International Congress on Environmental Planning and Management, VRCE Nagpur, India, 465-469, 1996.
    10.      Bhattacharya D. K., Reddy Y. H. S. and Dubey B., Multimedia in ecosystems modelling: Application to Keoladeo National Park, India, IASTED (The International Association of Science & Technology for Development) International Conference on Signal and Image Processing and Applications, Annecy, France, June 12-14, 1996, Paper # 241-109.
    11.  .  Shukla J. B., Dubey B. and Agarwal M., Modelling the depletion of forestry resource: Effects of Industrialization and population, Proc. International Congress on Modelling and Simulation, Australia, 2: 845-850, 1993.
    12.       Shukla J. B. and Dubey B., Effects of industrialization and pollution on forest ecosystem, Proc. International Congress on Modelling and Simulation, Australia, 2: 857-862, 1993.
    13. .    Shukla J. B., Dubey B. and Shukla A, Sustainable industrial development: A model, Proc. International Congress on Modelling and Simulation, Australia, 2: 997-1004, 1993.

       

      Publications in the Proceedings of National Conferences

    1.     Agarwal A. K., Dubey B., Sinha P. and Shukla J. B., Effects of two or more toxicants on a biological species: a non-linear mathematical model and its analysis, In Mathematical Analysis and Applications, Narosa Publishing House, New Delhi, India, p. 93-109, 2000.
    2.     Shukla J. B., Dubey B. and Shukla A., Effect of two cooperating populations on depletion of forestry resource, Proc. of Recent Trends in Industrial & Applied Mathematics, MACT Bhopal, P. 20-37, 1998.
    3.      Shukla J. B., Agarwal A., Naresh R. and Dubey B., Modelling the removal of pollutants from the atmosphere of an industrial city by monsoon rain, Proc. of Recent Trends in Industrial & Applied Mathematics, MACT Bhopal, p. 184-197, 1998
    4.      Dubey B., Effect of pollutant on biological species: A mathematical model, Proc. of Mathematical Modelling of Ecological and Environmental Systems, Jadavpur University, Calcutta, p. 15-22, 1995.
    5.      Agarwal M., Dubey B. and Shukla J. B., Modelling the depletion of forestry resource: Effects of industrialization and population, Proc. Indian Society of Industrial and Applied Mathematics (ISIAM’92), Roorkee, p. 287-290, 1993.



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