Dr. Mishra, an academician and researcher, embarked on his journey at ABV-IIITM Gwalior in July 2023, assuming the role of an Assistant Professor in the Department of Engineering Sciences. With a commendable record of over 3.5 years of postdoctoral experience at renowned global institutions, Dr. Mishra brings a profound wealth of knowledge to his current position.

Dr. Mishra earned PhD in applied mathematics with a specialization in mathematical ecology from the esteemed National Institute of Technology Raipur in March 2019. Prior to that, he obtained his M.Sc in Mathematics and Scientific Computing from MNNIT Allahabad. Notably, Dr. Mishra's academic journey includes the prestigious European ERCIM postdoc fellowship, which facilitated his postdoctoral research at the University of Warsaw, a prominent institution in the academic realm.

In March 2021, Dr. Mishra embarked on a new chapter in his academic journey, joining the Norwegian University of Life Sciences in Norway. During his tenure at this esteemed institution, he expanded his expertise, focusing on conceptual mathematical modeling for sustainable development. Here, he developed a profound background in slow-fast dynamical systems, adding an invaluable dimension to his research repertoire. Dr. Mishra also ventured into the intricate world of stochastic differential equations applied to biology, further enriching his multifaceted skill set and deepening his contributions to the field.

Dr. Mishra's research pursuits are marked by a passionate focus on mathematical modeling of natural systems, with a special emphasis on the field of life sciences. His expertise shines in the realm of dynamical systems modeling, enabling him to delve deep into complex sustainability issues intertwined with ecology and the environment. His primary research interests revolve around the captivating chemotaxis phenomenon observed in ecological species interactions, which he diligently explores through complex mathematical models.

In his scholarly endeavors, Dr. Mishra is driven by a profound curiosity, employing mathematical models that encompass differential equations, including ODEs, PDEs, and stochastic equations. He is particularly dedicated to unraveling the mysteries of these equations, deciphering their large-time behavior, stability, bifurcation of solutions, and their intricate connections with real-world systems. Furthermore, he applies his mathematical acumen to conduct numerical simulations, providing valuable insights into the approximation of solutions.

Dr. Mishra's academic contributions extend beyond his research, as he has actively participated in and presented talks at numerous national and international conferences, sharing his valuable insights and fostering intellectual exchange within the academic community. His dedication to advancing the frontiers of mathematical ecology and dynamical systems modeling exemplifies his commitment to the pursuit of knowledge and the betterment of our understanding of the natural world.

Note: PhD positions are available at Department of Engineering Sciences (Mathematics/Physics). Contact me if you are interested in mathematical biology.  Applications of PhD are invited in May and November each year. 

• Assistant Professor Grade-II at Department of Engineering Sciences, ABV-IIITM Gwalior from July 3, 2023 to Till date. 
• Postdoctoral fellow at Faculty of Science and Technology (REALTEK), Norwegian University of Life Sciences NMBU Norway from March 1, 2021 to June 30, 2023.
• ERCIM Postdoctoral fellow at Faculty of Mathematics, Informatics and Mechanics, University of Warsaw Poland from October 1, 2019 to February 28, 2021.

Administrative Positions:

• Faculty-in-charge sports at ABV-IIITM Gwalior from July 2023 to April 2024.
• Faculty coordinator sports at ABV-IIITM Gwalior from April 2024 to till date.

Subject Taught: 

• Engineering Mathematics (ES-102)
• Mathematics IV (IMAS-2201)
• Modeling and Simulation (IMAS-3201)

Publications:

1. P. Mishra, D. Wrzosek, Schoener-Polis-Holt’s model of the intraguild predation with predator taxis and repulsive chemotaxis. Accepted in Discrete and Continuous Dynamical Systems - Series B, 29 (12) (2024). Q1-SCI, MCQ:1.1.
2. P. Mishra, A. Ponossov and J. Wyller. On the dynamics of predator–prey models with role reversal. Physica D: Nonlinear Phenomena (2024): 134100.     https://doi.org/10.1016/j.physd.2024.134100. Q1-SCI, MCQ:1.08
3. P. Mishra, D. Wrzosek, Pursuit-Evasion Dynamics for Bazykin-Type Predator-Prey Model with Indirect Predator Taxis. Journal of Differential Equations 361 (2023)  https://doi.org/10.1016/j.jde.2023.02.063. Q1-SCI, MCQ:2.00.
4. 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. https://doi.org/10.1111/nrm.12363. Q2-SCIE, MCQ: 0.13.
5. 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. https://doi.org/10.1142/S0218202522500014. Q1-SCI, MCQ: 2.77.
6. 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.  https://doi.org/10.1016/j.aml.2021.107745. Q1-SCI, MCQ:1.17.
7. Mishra and B. Tiwari. Drivers of pattern formation in a predator-prey system with defense in fearful prey. Nonlinear Dynamics 105 (2021).  https://doi.org/10.1007/s11071-021-06719-2. Q1-SCI, MCQ:0.81.
8.  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. Q2-SCIE, MCQ: 0.21.
9. 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.Q1-SCI, MCQ:0.81.
10. 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. Q3-SCIE, MCQ: 0.37.
11. 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. Q1-SCIE, MCQ:0.27.
12.  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
13. 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
14. 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.
15. 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
16. 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-
17. 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
18. 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. FIG grant of INR 9.74 Lakhs for two years from ABV-IIITM Gwalior. (Nov 2023-Nov 2025)
2. 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
3. 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)
4. 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.
5. 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)
6. ERCIM Alain Bensoussan Fellowship from Oct 1, 2019-Feb 28, 2021

Selected Conferences and Talks:

1. CONTRIBUTED TALK entitled "Chemical Signalling and Pattern Formation in Predator-Prey Models" at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) in Waseda University, Tokyo, Japan August 20-25, 2023.
2. INVITED TALK entitled " Chemotaxis and Pattern Formation in Ecological Models" at International seminar on Mathematical Modeling and Turing Pattern Formation organized at School of Advanced Sciences, VIT Vellor India. September 11-15, 2023.
3. 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
4. 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.
5. 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).
6. 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)
7. Virtual talk on "The role of indirect prey-taxis and interference among predators in pattern formation" at RUDN University Russia on 11 February 2021.
8.  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
9. INVITED TALK entitled " Nonlinear Differential Equations and its Application" at Teerthanker Mahaveer University, Moradabad, India on 16 June 2020 (Online)
10. 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.