Dr. Mishra joined ABV-IIITM Gwalior in July 2023 as an Assistant Professor at the Department of Engineering Sciences.  With over 3.5 years of postdoctoral experience from prestigious global universities, he brings a wealth of knowledge to his role. Dr. Mishra’s research specializes in mathematical modeling of natural systems, particularly in the realm of life sciences. His expertise lies in the realm of dynamical systems modeling, through which he delves into sustainability issues intertwined with ecology and the environment. He is passionate about exploring the fascinating chemotaxis phenomenon observed in ecological species interactions through the mathematical models. Mathematical models of his interest concern the study of differential equations (ODE, PDE & Stochastic), such as their large time behavior, stability, and bifurcation of solutions and their links with real-world systems, as well as numerical simulations to approximate their solutions.

Publications:

1. P. Mishra, Wrzosek, Dariusz. Pursuit-Evasion Dynamics for Bazykin-Type Predator-Prey Model with Indirect Predator Taxis. Journal of Differential Equations 361 (2023) SCI. https://doi.org/10.1016/j.jde.2023.02.063
2. H. Bergland, P. Mishra, P.A. Pedersen, A. Ponossov and J. Wyller. Time delays and pollution in an open access fishery. Natural Resource Modeling (2022), 1-39. SCIE https://doi.org/10.1111/nrm.12363
3. P. Mishra and D. Wrzosek. Repulsive chemotaxis and predator evasion in predator prey models with diffusion and prey taxis. Mathematical Models and Methods in Applied Sciences 32 (2022), 1-42.  SCI https://doi.org/10.1142/S0218202522500014
4. P. Mishra and D. Wrzosek. Indirect taxis drives spatio-temporal patterns in an extended Schoener’s intraguild predator-prey model. Applied Mathematics Letters 125 (2021), 107745. SCI https://doi.org/10.1016/j.aml.2021.107745
5. Mishra and B. Tiwari. Drivers of pattern formation in a predator-prey system with defense in fearful prey. Nonlinear Dynamics 105 (2021). SCI https://doi.org/10.1007/s11071-021-06719-2
6.  S.N. Raw, P. Mishra, B. Tiwari. B.P. Sarangi. Appearance of temporal and spatial chaos in an ecological system: A Mathematical Modeling Study. Iranian Journal of Science and Technology, Transactions A: Science 45 (2021) SCI https://doi.org/10.1007/s40995-021-01139-8
7. S.N. Raw and B. Tiwari and P. Mishra. Qualitative analysis of a predator-prey system with double Allee effect and schooling behaviour. Nonlinear Dynamics 102(10)(2020). SCI. https://doi.org/10.1007/s11071-020-06018-2
8. S.N. Raw and B. Tiwari and P. Mishra. Analysis of a plankton-fish model with external toxicity and non-linear harvesting. Ricerche Da Mathematica Vol. 69 (2020). SCIE. https://doi.org/10.1007/s11587-019-00478-4
9. P. Mishra, S.N. Raw, B. Tiwari. On the dynamics of a cannibalistic predator-prey model with defense and diffusion. Applied Mathematical Modelling 90 (165-190) (2020). SCIE https://doi.org/10.1016/j.apm.2020.08.060
10.  S.N. Raw and P. Mishra, B. Tiwari, Mathematical study about a predator-prey model with anti-predator behavior. International Journal of Applied and Computational Mathematics Vol. 6 (1-22) (2020). SCOPUS. https://doi.org/10.1007/s40819-020-00822-5
11. P. Mishra and D. Wrzosek. The role of indirect prey-taxis and interference among predators in pattern formation. Mathematical Methods in Applied Sciences Vol. 43(18) (2020). SCIE https://doi.org/10.1002/mma.6426
12. S.N. Raw and B. Tiwari and P. Mishra. Dynamical complexities and pattern formation in an eco-epidemiological model with prey infection and harvesting. Journal of Applied Mathematics and Computing. Vol. 64 (17-52) (2020). SCIE https://doi.org/10.1007/s12190-020-01342-715.
13. P. Mishra, S.N. Raw and B. Tiwari. Study of a diffusive Leslie-Grower predator-prey system with mutual interference of predators and prey defense. Chaos, Solitons and Fractals. Vol. 120 (2019). SCI https://doi.org/10.1016/j.chaos.2019.01.012
14. P. Mishra, S.N. Raw. Dynamical complexities in a predator-prey model involving team of two prey and one predator. Journal of Applied Mathematics and Computing. Vol. 61 (1-2) (2019) ,SCIE https://doi.org/10.1007/s12190-018-01236-
15. S.N. Raw and P. Mishra. Modeling and analysis of inhibitory effect in the plankton-fish model: Application to Swarjedski Lake, Western Poland. Nonlinear Analysis: Real World Application. Vol. 46 (2019). SCI https://doi.org/10.1016/j.nonrwa.2018.09.026
16. S.N. Raw, P. Mishra, R. Kumar, S. Thakur. Complex dynamics of prey-predator system exhibiting group defense: A mathematical modeling study. Chaos, Solitons and Fractals. Vol. 100 (2017). SCI https://doi.org/10.1016/j.chaos.2017.05.010

Grants and Funding:

1. Travel grant of NOK 25800 from Norwegian University of Life Sciences Norway to attend the Third International Nonlinear Dynamics Conference (NODYCON 2023), organized by Sapienza University of Rome, Italy June 18-22, 2023
2. International travel grant of NOK 195000 (approx. 18100 Euro) from the Norwegian University of Life Sciences NMBU Norway for the research exchange stay in the University of Leicester, UK during July, 2023-November 2023 (Not Availed)
3. Partial funding (80 Euro/Diem) for 4 day stay at Erwin Schrödinger International Institute for Mathematics and Physics (ESI) of the University of Vienna to participate in the Kyoto-Vienna Workshop of the Thematic Programme on “Mathematical Methods for the Study of Self-organization in the Biological Sciences” from December 1 to 2, 2022.
4. Research exchange (with Inria Dracula Team) funding to 1 week stay upto 1500 Euro by ERCIM - the European Research Consortium for Informatics and Mathematics (not availed due to Covid-19 restrictions)
5. ERCIM Alain Bensoussan Fellowship from Oct 1, 2019-Feb 28, 2021

Selected Conferences and Talks:

1. A CONTRIBUTED TALK entitled "Chemical Signalling and Pattern Formation in Schoener’s Predator–Prey Model" at the Third International Nonlinear Dynamics Conference (NODYCON 2023) in Sapienza University of Rome, Rome, Italy. June 18-22, 2023
2. CONTRIBUTED TALK entitled " Modelling chemical signalling and chemotaxis in predator-prey systems" in the National Symposium on Implementation and Applications of Mathematics in Real Life held at VIT Vellore (iMPLEMATHATION 2023), 8-12th May 2023.
3. CONTRIBUTED TALK entitled "The role of indirect predator-taxis in an extended Schoener’s intraguild predator-prey model " during the 13th DSABNS 2022 conference at the Basque Center for Applied Mathematics (BCAM) and held on February, 8-11, 2022 (Virtual).
4. INVITED talk on "Application of Mathematics in Ecological Sustainability" in the five days webinar from on the theme, “Industrial Mathematics and Scientific Computing” at the Department of Mathematics, BMSIT& M, Bengaluru on 10th January 2022 (Virtual)
5. Virtual talk on "The role of indirect prey-taxis and interference among predators in pattern formation" at RUDN University Russia on 11 February 2021.
6.  Contributed Talk on "Pattern formation in a predator-prey model with defence in fearful prey " at a virtual international conference "Dynamics of biological systems: from viruses to populations" organized by Jagiellonian University, Kraków Poland on 25 September 2020
7. INVITED TALK entitled " Nonlinear Differential Equations and its Application" at Teerthanker Mahaveer University, Moradabad, India on 16 June 2020 (Online)
8. Given a talk on "Role of indirect-prey taxis and mutual interference among predator in pattern formation" at the Institute of Applied Mathematics and Mechanics, University of Warsaw Poland on 10 June 2020.