PhD Mathematics (2014-2018) Abdus Salam School of Mathematical Sciences, GC University, Lahore Pakistan.
MPhil Mathematics (2012-2014) Abdus Salam School of Mathematical Sciences, GC University, Lahore Pakistan.
MSc Mathematics (2010-2012) Quaid-e-Azam University, Islamabad.
09/2021–present Assistant Professor, Department of Mathematics, Air University Islamabad, Multan Campus.
11/2018–06/2021Assistant Professor, Department of Mathematics, NCBA&E Rahim Yar Khan Campus
04/2018–11/2018Assistant Professor, Department of Mathematics, Institute of Southern Punjab, Multan.
Journal Papers
Ahmed, R., Khan, A. Q., Amer, M., Faizan, A., & Ahmed, I. (2024). Complex Dynamics of a Discretized Predator–Prey System with Prey Refuge Using a Piecewise Constant Argument Method. International Journal of Bifurcation and Chaos, 2450120.
Tahir, N., Ahmed, R., & Shah, N. A. (2024). Complex dynamics of a discrete-time Leslie–Gower predator–prey system with herd behavior and slow–fast effect on predator population. International Journal of Biomathematics, 2450040, 26.
Naik, P. A., Javaid, Y., Ahmed, R., Eskandari, Z., & Ganie, A. H. (2024). Stability and bifurcation analysis of a population dynamic model with Allee effect via piecewise constant argument method. Journal of Applied Mathematics and Computing, 1-30.
Ahmed, R., Tahir, N., & Ali Shah, N. (2024). An analysis of the stability and bifurcation of a discrete-time predator–prey model with the slow–fast effect on the predator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(3).
Suleman, A., Qadeer Khan, A., & Ahmed, R. (2024). Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator. Mathematical Methods in the Applied Sciences, 47(11), 8561-8580.
Abbas, N., & Ahmed, R. (2024). Stability and bifurcation analysis of a discrete Leslie predator-prey model with fear effect. VFAST Transactions on Mathematics, 12(1), 16-29.
Imran, M., Almatrafi, M. B., & Ahmed, R. (2024). Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with harvesting effect. Commun. Math. Biol. Neurosci., 2024, Article-ID 11.
Alsubhi, M., Ahmed, R., Alraddadi, I., Alsharif, F., & Imran, M. (2024). Stability and bifurcation analysis of a discrete-time plant-herbivore model with harvesting effect. AIMS Mathematics, 9(8), 20014-20042.
Naik, P. A., Amer, M., Ahmed, R., Qureshi, S., & Huang, Z. (2024). Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect. Mathematical Biosciences and Engineering, 21(3), 4554-4586.
Aldosary, S. F., & Ahmed, R. (2024). Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method. AIMS Math, 9, 4684-4706.
Ahmed, R., Yazdani, M. S., & Saher, S. (2023). Complex dynamics of a predator-prey model with harvesting effects on both predator and prey. International Journal of Nonlinear Analysis and Applications, 14(10), 95-106.
Ahmed, R., & Almatrafi, M. B. (2023). Complex dynamics of a predator-prey system with Gompertz growth and herd behavior. International Journal of Analysis and Applications, 21, 100.
Shahzad, M. A., & Ahmed, R. (2023). Dynamic complexity of a discrete predator-prey model with prey refuge and herd behavior. VFAST Transactions on Mathematics, 11(1), 194-216.
Ahmed, R., & Akhtar, S. (2023). Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Universal Journal of Mathematics and Applications, 6(1), 30-42.
Ahmed, R., Akhtar, S., Farooq, U., & Ali, S. (2023). Stability, bifurcation, and chaos control of predator-prey system with additive Allee effect. Commun. Math. Biol. Neurosci., 2023, Article-ID 9.
Suleman, A., Ahmed, R., Alshammari, F. S., & Shah, N. A. (2023). Dynamic complexity of a slow-fast predator-prey model with herd behavior. AIMS Mathematics, 8(10), 24446-24472.
Ahmed, R., Rafaqat, M., Siddique, I., & Arefin, M. A. (2023). Complex Dynamics and Chaos Control of a Discrete‐Time Predator‐Prey Model. Discrete Dynamics in Nature and Society, 2023(1), 8873611.
Khabyah, A. A., Ahmed, R., Akram, M. S., & Akhtar, S. (2023). Stability, bifurcation, and chaos control in a discrete predator-prey model with strong allee effect. AIMS Mathematics, 8(4), 8060-8081.
Ahmed, R., Mushtaq, J., Saher, S., & Saeed, H. M. A. (2022). Dynamic analysis of a predator-prey model with Holling type-II functional response and prey refuge by using a NSFD scheme. Commun. Math. Biol. Neurosci., 2022, Article-ID 111.
Ahmed, R., Ahmad, A., & Ali, N. (2022). Stability analysis and Neimark-Sacker bifurcation of a nonstandard finite difference scheme for Lotka-Volterra prey-predator model. Commun. Math. Biol. Neurosci., 2022, Article-ID 61.
Ahmed, R., & Yazdani, M. S. (2022). Complex dynamics of a discrete-time model with prey refuge and Holling type-II functional response. J. Math. Comput. Sci., 12, Article-ID 113.
S. Akhtar, R. Ahmed, M. Batool, N. A. Shah, J. D. Chung (2021). Stability, bifurcation and chaos control of a discretized Leslie prey-predator model, Chaos, solitons and fractals, 152, 111345. DOI: https://doi.org/10.1016/j.chaos.2021.111345
R. Ahmed, S. Akhtar, M. Mukhtar, F. Anwar (2021). Bifurcation and Chaos Control of a System of Rational Difference Equations. Results in Nonlinear Analysis, 4(3), 169-178.
R. Ahmed (2020). Complex dynamics of a fractional-order predator-prey interaction with harvesting. Open journal of discrete applied mathematics, 3(3), 24-32
S. Liu, C. Gao, P. Yan, R. Ahmed, N. Javaid, M. Rafaqat (2020). Topological-based comparison and computer-based analysis of TUC4[m,n], TUZC6[m,n], TUAC6[m,n] nanotubes. Mathematical methods in the applied sciences. DOI:
M. Rafaqat, R. Ahmed, T. Donchev, V. Lupulescu (2017). Filippov-Pliss lemma for dynamical inclusions on time scale. Advances in difference equations. 2017-302, DOI: 10.1186/s13662-017-1360-6.
R. Ahmed, T. Donchev, A. I. Lazu (2017). Nonlocal m-dissipative evolution inclusions in general banach spaces. Mediterranean journal of mathematics. (2017) 14:215, DOI: 10.1007/s00009-017-1016-5.
R. Ahmed, T. Donchev, A. I. Lazu, A. Nosheen, M. Rafaqat (2016). On the Solution Set of Multivalued Fuzzy Fractional Systems. International journal of pure and applied mathematics. 109(1), 49-66.
T. Donchev, A. Nosheen, R. Ahmed (2015). On the Solution Set of Fuzzy Systems. Contemporary methods in mathematical physics and gravitation, 1(2), 55-70.
O. Carja, T. Donchev, M. Rafaqat, R. Ahmed (2014.) Viability of Fractional Differential Inclusions. Applied mathematics letters, 38, 48-51.
>>>
Undergraduate Courses
Pre-Calculus
Multivariable Calculus
Discrete Mathematics
Functional Analysis
Calculus and Analytical Geometry
Complex Analysis
Partial Differential Equations
Ordinary Differential Equations
Vector and Tensor Analysis
Differential Geometry
Introduction to Basic Linear and Nonlinear Optimization
Linear Algebra
Group Theory
Graduate Courses
Applied Partial Differential Equations
Research Methodology
Nonlinear Dynamics and Chaos
Advanced Statistical Techniques
Mathematical Modeling and Simulation
Mphill Students
Saqib Yazdani
Yashra Javaid
Naheed Tahir
Muhammad Asim Shahzad
Ahmad Suleman
Muhammad Amir
Muhammad Imran
Naqi Abbas
Syad Qaisar Shahzad
Hafsa Shafique
PhD Students
Arshad Mehmood (in progress)
Jawad Afzal (in progress)