NILESH KUMAR THAKUR

Department Department of Mathematics
Designation Associate Professor
Educational Qualification M. Phil., Ph. D. (IIT (ISM) Dhanbad)
E-Mail nkthakur.maths@nitrr.ac.in
Contact Number 7772078448
Areas of Interest

Mathematical Ecology, Mathematical Modelling, Nonlinear Dynamics.

Publications

Published in International Journals:

  1.  Singh, R., Chauhan, R. P., Kumar, A. and Thakur, N. K. (2025) Analysis of fractional-order Leslie-Gower model incorporating M-H type functional response and fear effect. Iranian Journal of Science (Accepted).
  2. Sinha N. and Thakur, N. K. (2025) Impact of hunting cooperation and fear on a delayedEco-epidemiological model with disease in predator. Nonlinear Science, 5, 100066.
  3. Ojha, A., Mandal, S., Singh, R., Thakur, N. K., Tiwari, P. K. (2025) Predator–prey dynamics in autonomous and nonautonomous settings: Impacts of anti-predator behavior, refuge, and additional food. Chaos, Solitons and Fractals, 196, 116409.
  4. Chauhan, R. P., Singh, R., Kumar, A. and Thakur, N. K. (2024) Role of prey refuge and fear level in fractional prey–predator model with anti-predator. Journal of Computational Science, 81, 102385.
  5. Singh, R., Ojha, A., Thakur, N. K. and Upadhyay, R. K. (2024) Delay-induced nutrient recycling in plankton system:Application to Sundarban mangrove wetland. Nonlinear Analysis: Modelling and Control, 29 (3), 562-587.
  6. Singh, R., Ojha, A., and Thakur, N. K. (2024) Modeling the effect of interference and gestation delay in an interacting good biomass and bird population: An application to wetland ecosystem. Thalassas: An International Journal of Marine Sciences, 40, 539–556.
  7. Srivastava, S. C., Thakur, N. K., Singh, R. and Ojha, A. (2024) Impact of fear and switching on a delay-induced eco-epidemiological model with Beverton–Holt functional response. International Journal of Dynamics and Control, 12, 669-695.
  8. Thakur, N. K., Srivastava, S. C. and Ojha, A. (2023) A comprehensive study of spatial spread and multiple time delay in an eco-epidemiological model with infected prey. International Journal of Modeling, Simulation, and Scientific Computing (Accepted). 
  9. Singh, R., Ojha, A., Tiwari, P. K., Thakur, N. K. and Kang, Y (2023) Impact of time delay in a plankton-fish system with nonlinear harvesting and external toxicity. International Journal of Biomathematics (Accepted).
  10. Kumar, S., Singh, R., Chauhan, R. P. and Thakur, N. K. (2023) Investigation of an interacting Fractional-Order predator–prey system in presence of fear and harvesting. Iranian Journal of Science, 47, 1739-1749.
  11. Ojha, A. and Thakur, N. K. (2023) Complex dynamics induced by multiple gestation delays in a Leslie–Gower-type system with competitive interference. Math Meth Appl Sci. (Accepted).
  12. Srivastava, S. C. and Thakur, N. K. (2023) Modeling the spread and control of vral infection in damaged aquatic system: Emergence of patterns.  Iran J Sci Technol Trans Sci., 47, 467-487.
  13. Singh, R., Tiwari, S. K., Ojha, A. and Thakur, N. K. (2023) Dynamical study of nutrient-phytoplankton model with toxicity: Effect of diffusion and time delay. Math Meth Appl Sci., 46, 490-509.
  14. Thakur, N. K., Singh, R. and  Ojha, A. (2022) Dynamical study of harmful algal bloom in Sundarban mangrove wetland with spatial interaction and competing effects. Modeling Earth Systems and Environment 8, 555-577.
  15. Ojha, A. and Thakur, N. K. (2021) Delay-induced Hopf and double Hopf-bifurcation in plankton system with dormancy of predators. Nonlinear Dynamics 105, 997-1018.
  16. Tiwari, S. K., Singh, R. and Thakur, N. K. (2021) Dynamical study of infochemical influences on tropic interaction of diffusive plankton system. SN Applied Sciences  3, 301.
  17. Thakur, N. K., Srivastava, S. C. and Ojha, A. (2021) Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity. Iran J Sci Technol Trans Sci. 45, 283-304.                          
  18. Thakur, N. K., Ojha, A., Tiwari, P. K. and Upadhyay, R. K. (2021) An investigation of delay induced stability transition in nutrient-plankton systems. Chaos, Solitons and Fractals 142, 110474.
  19. Ojha, A. and Thakur, N. K. (2020)  Exploring the complexity and chaotic behavior in plankton–fish system withmutual interference and time delay. BioSystems 198, 104283.
  20. Thakur, N. K., Ojha, A., Jana, D. and Upadhyay, R. K. (2020) Modeling the Plankton-Fish Dynamics with Top Predator Interference and Multiple Gestation Delays. Nonlinear Dynamics 100, 4003-4029. 
  21. Thakur, N. K. and Ojha, A. (2020) Complex Dynamics of Delay‑Induced Plankton-Fish Interaction Exhibiting Defense. SN Applied Sciences  2, 1114.
  22. Thakur, N. K. and Ojha, A. (2020) Complex plankton dynamics induced by adaptation and defense. Modeling Earth Systems and Environment 6, 907-916.
  23. Thakur, N. K. and Gupta, R. (2017) Analysis of complex wetland ecological system: Effect of harvesting. Computational Ecology and Software 7 (4), 140-152.
  24. Thakur, N. K., Tiwari, S. K., Dubey, B and Upadhyay, R. K. (2017) Diffusive Three Species Plankton Model in the Presence of Toxic Prey: Application to Sundarban Mangrove Wetland. Journal of Biological Systems 25 (2), 1-22.
  25. Thakur, N. K., Gupta, R. and Upadhyay, R. K. (2017) Complex Dynamics of Diffusive Predator-Prey System with Beddington-DeAngelis functional response: The role of Prey-Taxis. Asian-European Journal of Mathematics 10 (1), 1750047, 1-15.
  26. Thakur, N. K., Tiwari, S. K. and Upadhyay, R. K. (2016) Harmful algal blooms in fresh and marine water systems: The role of toxin producing phytoplankton. International Journal of Biomathematics 9 (3), 1650043.
  27. Thakur, N. K., Gupta, R. and Upadhyay, R. K. (2015) Turing and Non-Turing patterns in diffusive plankton model. Computational Ecology and Software 5 (1), 16-27.
  28. Upadhyay, R. K., Patra, A., Dubey, B. and Thakur, N. K. (2014) A Predator-Prey Interaction Model with Self and Cross Diffusion in Aquatic Systems. Journal of Biological Systems 22 (4), 1-22.
  29. Parshad, R. D., Upadhyay, R. K. and Thakur, N. K. (2012) On the Well Posedness and Further Regularity of a Diffusive Three Species Aquatic Model. Applied Mathematical Sciences 6 (3), 597-619.
  30. Rai, V., Upadhyay, R. K. and Thakur, N. K. (2012) Complex Population Dynamics in Heterogeneous Environments: Effects of Random and Directed Animal Movements. International Journal of Nonlinear Sciences and Numerical Simulation, 13, 299-309.
  31. Upadhyay, R. K., Volpert, V. and Thakur, N. K. (2012) Propagation of Turing patterns in a plankton model. Journal of Biological Dynamics 6 (2), 524-538.
  32. Upadhyay, R. K., Thakur, N. K. (2012) Spatiotemporal pattern induced by self and cross-diffusion in a spatial Holling-Tanner model. Computational Ecology and Software 2 (1), 1-25.
  33. Upadhyay, R. K., Thakur, N. K. and Rai, V. (2011) Diffusion-driven instabilities and spatio-temporal patterns in an aquatic predator-prey system with Beddington-DeAngelis type functional response. International Journal of Bifurcation and Chaos 21 (3), 663-684.
  34. Upadhyay, R. K., Wang, W. and Thakur, N. K. (2010) Spatiotemporal Dynamics in a Spatial Plankton System. Mathematical Modelling of Natural Phenomena 5 (5), 101-121.
  35. Upadhyay, R. K., Thakur, N. K. and Dubey, B. (2010) Nonlinear non-equilibrium pattern formation in a spatial aquatic system. Journal of Biological Systems 18 (1), 129-159.

 

Published in National and International Conferences:

  1. Srivastava, S.C. and Thakur, N.K. (2023). Dynamical Study of an Epidemiological Model with Harvesting and Infection in Prey Population. Frontiers in Industrial and Applied Mathematics. FIAM 2021. (Springer Proceedings in Mathematics & Statistics, vol 410. Springer, Singapore), 395-409.
  2. Thakur, N. K., Ojha, A. and Tiwari, S. K. (2020) The Role of Adaptation in Plankton System with Beddington-DeAngelis Type Functional Response. Mathematical Modelling and Scientific Computing with Applications (Springer Proceedings in Mathematics & Statistics), 21-33.
  3. Thakur, N. K., Upadhyay, R. K. and Raw, S. N. (2012) Instabilities and Patterns in Zooplankton-Phytoplankton Dynamics: Effect of Spatial Heterogeneity. Communications in Computer and Information science (Springer-Verlag Berlin Heidelberg), 229-236.
  4. Raw, S. N., Upadhyay, R. K. and Thakur, N. K. (2012) Crisis-Limited Chaotic Dynamics in an Eco-epidemiological System of the Salton Sea.Communications in Computer and Information science (Springer-Verlag Berlin Heidelberg), 201-209.
Other Info.

Conference/Seminar/Workshop   

  • Guest speaker at Seminar focused on the topic of Mathematics (Qualitative Analysis of Ordinary Differential Equation), 11th November, 2024, Disha College Raipur, Chhattisgarh, India.
  • Invited talk in International Seminar on Mathematical Modeling and Turing's Pattern Formation,, 15th September, 2023, VIT Vellore, Tamil Hadu, India.
  • Expert talk in the AICTE-QIP on Implementation of Numerical Mehtods using MATLAB, 03-08 January, 2022, IIT Indore, Madhya Pradesh, India.
  • Chaired a Technical Session in the 3rd International Conference on Frontiers in Industrial and Applied Mathematics, 21-22 December, 2020, NIT Jamshedpur, Jharkhand, India.
  • Invited talk in International Conference on Differential Equations and Control Problems: Modeling, Analysis and Computations, 17-19 June, 2019, IIT Mandi, Himachal Pradesh, India.
  • Presented a research paper in International Conference on Mathematical Modelling and Scientific Computing with Applications, 19-21 July, 2018, IIT Indore, Madhya Pradesh, India.
  • Presented a research paper in International Congress of Mathematician, 19-27 August, 2010, Hyderabad, India.
  • Attended a workshop on Advanced Numerical Techniques and Applications, June 29-July 11, 2009, Banaras Hindu University, Varanasi, Uttar Pradesh, India.
  • Participated in International conference on Mathematical Modelling and Computer Simulation, 2006, LNMIT, Jaipur, Rajasthan, India.

Research Projects:

  1. Modeling and Analysis of Fractional Order Predator-Prey System: A Mathematical Approach, SERB (MATRICS), India, 2023-2026.
  2. Dynamical Study of Delay-Induced Stability and Chaos in Plankton Population, SERB (CRG), India, 2018-2021.
  3. Modelling Pattern Formation in Spatial Aquatic Systems: Mathematical Models and Applications, Chhattisgarh Council of Science & Technology, Raipur, Chhattisgarh, India, 2015-2018.

Ph. D. Guidance:  

Completed:

  1. Smriti Chandra Srivastava, Dynamical Study of Complex Eco-epidemiological System: A Mathematical Modeling Approach, 2024.
  2. Ravikant Singh, Conservation of degraded wetland ecosystem: A mathematical  modeling, 2023.
  3. Archana Ojha, Modelling delay-induced stability and chaos in population dynamics, 2021.
  4. Rashi Gupta, Mathematical modelling of complex ecological systems: Models and methods, 2018.

 In Progress:

  1. Nisha Sinha 
  2. Hema
  3. Kajal Mishra

M.Sc. (Dissertation) Guidance:

  1. Bhankumari Anchal, Sustainability Assessment of Wetland Ecosystem: Á Mathematical Modeling, 2025.
  2. Akanksha Gupta, Modeling Spatial Spread and Patterns in Plankton System with Cross Diffusion, 2025.
  3. Vivek Kumar Gupta, Emergence of Pateerns in Heterogeneous Plankton System, 2024.
  4. Sayantani Biswas, Analysis of Viral Infections in Plankton System: A Mathematical Model, 2024.

 Courses Taught (For UG and PG):

  • Mathematics-I, Mathematics-II, Mathematics-III.
  • Numerical Methods
  • Ordinary Differential  Equation