SavedAdd your journal

Journals / Fundamental Journal of Mathematics and Applications / 2025 / Volume: 8 Issue: 4

A New Prey-Predator Modeling with Experimental Data for Biological Control of Couch Grass

Mehmet Yavuz(NECMETTIN ERBAKAN UNIVERSITY, FACULTY OF SCIENCE)0000-0002-3966-6518
Merve Başaçık(NECMETTIN ERBAKAN UNIVERSITY, FACULTY OF SCIENCE)0009-0000-3473-9127
Ayşe Nur Yaman(NECMETTIN ERBAKAN UNIVERSITY, FACULTY OF SCIENCE)0009-0009-2849-8983
Pages
—
Publication Date
2025-12-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The numerical simulations are carried out using the fourth-order Runge–Kutta method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new three-dimensional predator–prey model is developed, consisting of one prey and two predators.
📊
Key Findings & Data:Through these simulations, the interactions between two populations are examined by varying the initial planting rates/numbers of radish and couch grass, and the dynamic changes of the populations over time are analyzed.
💡
Conclusion & Impact:The numerical simulations are carried out using the fourth-order Runge–Kutta method.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Couch grass · Radish · Herbivores

Abstract

In this study, a new three-dimensional predator–prey model is developed, consisting of one prey and two predators. The aim of the model is to reduce or eliminate the target weed species through natural means. One of the novelties of the study is that one of the predators is the radish plant, and the model parameters are obtained from real data. The primary objective of the study is to investigate the natural suppression or eradication of the harmful weed species using the constructed predator–prey framework, supported by numerical simulations. Through these simulations, the interactions between two populations are examined by varying the initial planting rates/numbers of radish and couch grass, and the dynamic changes of the populations over time are analyzed. Furthermore, the model and its solutions are interpreted within the context of mathematical biology. The equilibrium points are determined, followed by numerical solutions of the three-dimensional system, and corresponding simulations are performed. The numerical simulations are carried out using the fourth-order Runge–Kutta method.

🔖

Cite This Article

Yavuz, M., Başaçık, M., Yaman, A. N. (2025). A New Prey-Predator Modeling with Experimental Data for Biological Control of Couch Grass. Fundamental Journal of Mathematics and Applications, Volume: 8 Issue: 4. https://doi.org/10.33401/fujma.1806523

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (37)

  1. A.F. Naser, M.B. Mahdi, F.H. Meqtoof and H.A. Etih, Modelling trip distribution using the gravity model and Fratar's method, Math. Modelling Eng. Probl., 8(2) (2021), 230–236. $ \href{ https://doi.org/10.18280/mmep.080209}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85105801178?origin=resultslist}{\mbox{[Scopus]}} $
  2. A. Elmas, G. Akyüz, A. Bergal, M. Andaç and Ö. Andaç, Mathematical modelling of drug release, Res. Eng. Struct. Mater., 6(4) (2020). $ \href{http://doi.org/10.17515/resm2020.178na0122}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85097436895?origin=resultslist}{\mbox{[Scopus]}} $
  3. D. Zos-Kior, O. Shkurupii, I. Hnatenko, O. Fedirets, I. Shulzhenko and V. Rubezhanska, Modeling of the investment program formation process of ecological management of the agrarian cluster, Eur. J. Sustain. Dev., 10(1) (2021), 571–571. $ \href{https://doi.org/10.14207/ejsd.2021.v10n1p571}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85101101382?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000625205000016}{\mbox{[Web of Science]}} $
  4. R. Sameni, Mathematical modeling of epidemic diseases; a case study of the COVID-19 coronavirus, arXiv preprint (2020). $ \href{https://doi.org/10.48550/arXiv.2003.11371}{\mbox{[CrossRef]}} $
  5. S. Cai, Z. Mao, Z. Wang, M. Yin and G.E. Karniadakis, Physics-informed neural networks (PINNs) for fluid mechanics: A review, Acta Mech. Sin., 37(12) (2021), 1727–1738. $ \href{https://doi.org/10.1007/s10409-021-01148-1}{\mbox{[CrossRef]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000745567800001}{\mbox{[Web of Science]}} $
  6. A. Deutsch, L. Brusch, H. Byrne, G. De Vries and H. Herzel, Mathematical Modeling of Biological Systems, Vol. I, (2007). $ \href{https://doi.org/10.1007/978-0-8176-4558-8}{\mbox{[CrossRef]}} $
  7. H. Joshi and M. Yavuz, A novel fractional-order model and analysis of cancer-immune system interaction in an avascular environment with an efficient control mechanism, J. Comput. Appl. Math., 473 (2026), 116888. $ \href{https://doi.org/10.1016/j.cam.2025.116888}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/105009914774?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001532762100001}{\mbox{[Web of Science]}} $
  8. H. Joshi and M. Yavuz, Chaotic dynamics of a cancer model with singular and non-singular kernel, Discrete Contin. Dyn. Syst.-S, 18(5) (2025), 1416–1439. $ \href{https://doi.org/10.3934/dcdss.2025016}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85219030849?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001515645300003}{\mbox{[Web of Science]}} $
  9. R. Geetha, M.Y. Muthurathinam Sivabalan, T. Megala and M.S. Pradeep, Biodiversity and ecosystem stability in a four-species prey-predator food chain with meta-communities, AIMS Bioeng., 12(4) (2025), 530–555. $ \href{https://doi.org/10.3934/bioeng.2025025}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/105021976631?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001610718600001}{\mbox{[Web of Science]}} $
  10. A. Ebrahimzadeh, A. Jajarmi and M. Yavuz, Fractional optimal control of anthroponotic cutaneous leishmaniasis with behavioral and epidemiological extensions, Math. Comput. Appl., 30(6) (2025), 122. $ \href{https://doi.org/10.3390/mca30060122}{\mbox{[CrossRef]}} $
  11. D.J.T. Nguefack, Mathematical modeling of schistosomiasis transmission using reaction-diffusion equations, Fundam. J. Math. Appl., 7(2) (2024), 118–136. $ \href{https://doi.org/10.33401/fujma.1412958}{\mbox{[CrossRef]}} $
  12. H. Nasir and A.A.M. Daud, Global dynamics and sensitivity analysis of a diabetic population model with two-time delays, Math. Modell. Numer. Simul. Appl., 5(1) (2025), 198–233. $ \href{https://doi.org/10.53391/mmnsa.1545744}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/105002480261?origin=resultslist}{\mbox{[Scopus]}} $
  13. H. Sahebi Fard, E. Dastranj and A. Jajarmi, A novel fractional stochastic model equipped with Y-Caputo fractional derivative in a financial market, Math. Methods Appl. Sci., 48(9) (2025), 9653–9661. $ \href{https://doi.org/10.1002/mma.10832}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/105000367360?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001446207500001}{\mbox{[Web of Science]}} $
  14. M.S. Akber, M.M. Hasan, M.H. Kabir and M.O. Gani, Population projection of Southeast Asia with a time-delay logistic model, Bull. Biomathematics, 3(1) (2025), 1–20. $ \href{https://doi.org/10.59292/bulletinbiomath.1707070}{\mbox{[CrossRef]}} $
  15. F. Evirgen, E. Uçar, S. Uçar and N. Özdemir, Modelling influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates, Math. Modell. Numer. Simul. Appl., 3(1) (2023), 58–73. $ \href{https://doi.org/10.53391/mmnsa.1274004}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85160237466?origin=resultslist}{\mbox{[Scopus]}} $
  16. S. Uçar, Analysis of hepatitis B disease with fractal–fractional Caputo derivative using real data from Turkey, J. Comput. Appl. Math., 419 (2023), 114692. $ \href{https://doi.org/10.1016/j.cam.2022.114692}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85139045577?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000863214300003}{\mbox{[Web of Science]}} $
  17. K. Türk and M. Gümüş, Stability analysis and simulations of the discrete-time cancer epidemic model, Fundam. J. Math. Appl., 8(3) (2025), 148–160. $ \href{https://doi.org/10.33401/fujma.1696954}{\mbox{[CrossRef]}} $
  18. M. Yavuz and N. Sene, Stability analysis and numerical computation of the fractional predator–prey model with the harvesting rate, Fractal Fract., 4(3) (2020), 35. $ \href{https://doi.org/10.3390/fractalfract4030035}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85089851294?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000578902500001}{\mbox{[Web of Science]}} $
  19. D. Ghosh, P.K. Santra and G.S. Mahapatra, A three-component prey-predator system with interval number, Math. Modell. Numer. Simul. Appl., 3(1) (2023), 1–16. $ \href{https://doi.org/10.53391/mmnsa.1273908}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85172871424?origin=resultslist}{\mbox{[Scopus]}} $
  20. P.A. Naik, Z. Eskandari, H.E. Shahkari and K. M. Owolabi, Bifurcation analysis of a discrete-time prey-predator model, Bull. Biomathematics, 1(2) (2023), 111–123. $\href{https://doi.org/10.59292/bulletinbiomath.2023006}{\mbox{[CrossRef]}} $
  21. A. Chatterjee and S. Pal, A predator-prey model for the optimal control of fish harvesting through the imposition of a tax, Int. J. Optim. Control: Theor. Appl., 13(1) (2023), 68–80. $ \href{https://doi.org/10.11121/ijocta.2023.1218}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85148606342?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000925933300002}{\mbox{[Web of Science]}} $
  22. P.A. Naik, Z. Eskandari, M. Yavuz and J. Zu, Complex dynamics of a discrete-time Bazykin–Berezovskaya prey-predator model with a strong Allee effect, J. Comput. Appl. Math., 413 (2022), 114401. $ \href{https://doi.org/10.1016/j.cam.2022.114401}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85130916387?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000811819000004}{\mbox{[Web of Science]}} $
  23. M.M. Maclean, D. J. Carslake, M. R. Evans, S. Townley and D. J. Hodgson, The usefulness of sensitivity analysis for predicting the effects of cat predation on the population dynamics of their avian prey, Ibis, 150 (2008), 100–113. $ \href{https://doi.org/10.1111/j.1474-919X.2008.00864.x}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/50049092729?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000259108700009}{\mbox{[Web of Science]}} $
  24. J. Danane, M. Yavuz and M. Yıldız, Stochastic modeling of three-species prey–predator model driven by Levy jump with mixed Holling-II and Beddington–DeAngelis functional responses, Fractal Fract., 7(10) (2023), 751. $ \href{https://doi.org/10.3390/fractalfract7100751}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85175162646?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001095309300001}{\mbox{[Web of Science]}} $
  25. H. Merdan and O. Duman, On the stability analysis of a general discrete-time population model involving predation and Allee effects, Chaos Solitons Fract., 40(3) (2009), 1169–1175. $ \href{https://doi.org/10.1016/j.chaos.2007.08.081}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/65349142508?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000266418000015}{\mbox{[Web of Science]}} $
  26. Z. Eskandari, P.A. Naik and M. Yavuz, Dynamical behaviors of a discrete-time prey-predator model with harvesting effect on the predator, J. Appl. Anal. Comput., 14 (2024), 283–297. $ \href{https://doi.org/10.11948/20230212}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85178871273?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001157081500001}{\mbox{[Web of Science]}} $
  27. T.K. Aydın and S.S. Durduran, Determining future scenarios of urban areas with cellular automata/Markov chain model method; example of Ereğli District Konya–Türkiye (2030–2040), Earth Sci. Inform., 17(3) (2024), 2679–2697. $ \href{https://doi.org/10.1007/s12145-024-01283-w}{\mbox{[CrossRef]}} $
  28. G.Q. Sun, L. Li, J. Li, C. Liu, Y.P. Wu, S. Gao and G. L. Feng, Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis, Phys. Life Rev., 43 (2022), 239–270. $ \href{https://doi.org/10.1016/j.plrev.2022.09.005}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85140775097?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000880139900003}{\mbox{[Web of Science]}} $
  29. M.S. Habibullah, B.H. Din, S.H. Tan and H. Zahid, Impact of climate change on biodiversity loss: Global evidence, Environ. Sci. Pollut. Res., 29(1) (2022), 1073–1086. $ \href{https://doi.org/10.1007/s11356-021-15702-8}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85111841075?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000680335200002}{\mbox{[Web of Science]}} $
  30. L.N. Guo, C. She, D.B. Kong, S.L. Yan, Y.P. Xu, M. Khayatnezhad and F. Gholinia, Prediction of the effects of climate change on hydroelectric generation, electricity demand, and emissions of greenhouse gases under climatic scenarios and optimized ANN model, Energy Rep., 7 (2021), 5431–5445. $ \href{https://doi.org/10.1016/j.egyr.2021.08.134}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85119001410?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000701734000013}{\mbox{[Web of Science]}} $
  31. B. Ringselle, B. De Cauwer, J. Salonen and J. Soukup, A review of non-chemical management of couch grass (Elymus repens), Agronomy, 10(8) (2020), 1178. $ \href{https://doi.org/10.3390/agronomy10081178}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85090881899?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000568165300001}{\mbox{[Web of Science]}} $
  32. S. Okrushko, Allelopathic effect of couch grass (Elymus repens L.) on germination of common wheat seeds, Zemdirbyste, 109(4) (2022), 323–328. $ \href{https://doi.org/10.13080/z-a.2022.109.041}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85145593785?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000907595900005}{\mbox{[Web of Science]}} $
  33. K.S. Torresen, B. Ringselle, L.O. Brandsaeter and J. Salonen, Autumn mowing and pelargonic acid can suppress Elymus repens abundance especially when combined with increased crop competition, Julius-K¨uhn-Archiv, (468) (2022). $\href{https://www.openagrar.de/servlets/MCRFileNodeServlet/openagrar_derivate_00044744/JKA_468_15.pdf}{\mbox{[CrossRef]}} $
  34. S. Mutlu, Predator-prey models and investigation of predator-prey Caputo fractional derivative, M.Sc. Thesis, Sakarya University, Sakarya, Türkiye, (2022). $ \href{https://acikerisim.sakarya.edu.tr/handle/20.500.12619/98773}{\mbox{[Web]}} $
  35. S. Yıldız, Local stability and bifurcation analysis of a Lotka–Volterra type discrete predator-prey model including refuge effect, M.Sc. Thesis, TOBB ETU, (2021). $ \href{https://koha.etu.edu.tr/cgi-bin/koha/opac-detail.pl?biblionumber=200444367&shelfbrowse_itemnumber=489195}{\mbox{[Web]}} $
  36. M.J. Uddin, S. M. S. Rana, S. Işık and F. Kangalgil, On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population, Chaos Solitons Fract., 175 (2023), 113932. $\href{https://doi.org/10.1016/j.chaos.2023.113932}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85171566105?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001068779300001}{\mbox{[Web of Science]}} $
  37. Z. Ali, F. Rabiei and K. Hosseini, A fractal–fractional-order modified predator–prey mathematical model with immigrations, Math. Comput. Simul., 207 (2023), 466–481. $\href{https://doi.org/10.1016/j.matcom.2023.01.006}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85146950654?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000924564800001}{\mbox{[Web of Science]}} $