790
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Incommensurate conformable-type three-dimensional Lotka–Volterra model: discretization, stability, and bifurcation

ORCID Icon, &
Pages 113-120 | Received 29 Sep 2021, Accepted 22 Apr 2022, Published online: 05 May 2022

References

  • Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66. doi:10.1016/j.cam.2014.10.016
  • Abu Arqub, O. (2018). Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm. Calcolo, 55(3), 1–28. doi:10.1007/s10092-018-0274-3
  • Ahmed, E., & Elgazzar, A. S. (2007). On fractional order differential equations model for nonlocal epidemics. Physica A, 379(2), 607–614. doi:10.1016/j.physa.2007.01.010
  • Ahmed, E., El-Sayed, A., & El-Saka, H. (2007). Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. Journal of Mathematical Analysis and Applications, 325(1), 542–553. doi:10.1016/j.jmaa.2006.01.087
  • Ali, I., Saeed, U., & Din, Q. (2019). Bifurcation analysis and chaos control in discrete-time system of three competing species. Arabian Journal of Mathematics, 8(1), 1–14. doi:10.1007/s40065-018-0207-7
  • Ali, K. K., Abd El Salam, M. A., Mohamed, E. M., Samet, B., Kumar, S., & Osman, M. S. (2020). Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series. Advances in Continuous and Discrete Models, 2020, 1–23.
  • Alquran, M., Yousef, F., Alquran, F., Sulaiman, T. A., & Yusuf, A. (2021). Dual-wave solutions for the quadratic-cubic conformable-Caputo time-fractional Klein-Fock-Gordon equation. Mathematics and Computers in Simulation, 185, 62–76. doi:10.1016/j.matcom.2020.12.014
  • Arqub, O. A., Osman, M. S., Abdel-Aty, A. H., Mohamed, A., & Momani, S. (2020). A numerical algorithm for the solutions of ABC singular Lane–Emden type models arising in astrophysics using reproducing kernel discretization method. Mathematics, 8(6), 923. doi:10.3390/math8060923
  • Diethelm, K., & Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229–248. doi:10.1006/jmaa.2000.7194
  • Djennadi, S., Shawagfeh, N., Osman, M. S., Gómez-Aguilar, J. F., & Arqub, O. A. (2021). The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique. Physica Scripta, 96(9):094006.
  • Du, M., Wang, Z., & Hu, H. (2013). Measuring memory with the order of fractional derivative. Scientific Reports, 3(1), 1–3.
  • Elsadany, A. A., & Matouk, A. E. (2015). Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization. Journal of Applied Mathematics and Computing, 49(1-2), 269–283. doi:10.1007/s12190-014-0838-6
  • Grove, E. A., & Ladas, G. (2004). Periodicities in nonlinear difference equations (Vol. 4). Boca Raton: CRC Press.
  • Gurcan, F., Kaya, G., & Kartal, S. (2019). Conformable fractional order lotka–volterra predator–prey model: Discretization, stability and bifurcation. J. Comput. Nonlinear Dynam, 14(11), 111007. doi:10.1115/1.4044313
  • Inan, B., Osman, M. S., Ak, T., & Baleanu, D. (2020). Analytical and numerical solutions of mathematical biology models: The Newell–Whitehead–Segel and Allen-Cahn equations. Mathematical Methods in the Applied Sciences, 43(5), 2588–2600. doi:10.1002/mma.6067
  • Jaradat, I., Alquran, M., Katatbeh, Q., Yousef, F., Momani, S., & Baleanu, D. (2020). An avant-garde handling of temporal-spatial fractional physical models. International Journal of Nonlinear Sciences and Numerical Simulation, 21(2), 183–194. doi:10.1515/ijnsns-2018-0363
  • Jaradat, I., Alquran, M., Yousef, F., Momani, S., & Baleanu, D. 2019). On (2+1)-dimensional physical models endowed with decoupled spatial and temporal memory indices. The European Physical Journal plus, 134(7), 360. doi:10.1140/epjp/i2019-12769-8
  • Jellison, B. M., Ninokawa, A. T., Hill, T. M., Sanford, E., & Gaylord, B. (2016). Ocean acidification alters the response of intertidal snails to a key sea star predator. Proceedings of the Royal Society B: Biological Sciences, 283(1833), 20160890. doi:10.1098/rspb.2016.0890
  • Kartal, S., & Gurcan, F. (2019). Discretization of conformable fractional differential equations by a piecewise constant approximation. International Journal of Computer Mathematics, 96(9), 1849–1860. doi:10.1080/00207160.2018.1536782
  • Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70. doi:10.1016/j.cam.2014.01.002
  • Korobeinikov, A., & Wake, G. C. (1999). Global properties of the three-dimensional predator–prey Lotka–Volterra systems. Journal of Applied Mathematics Decision Sciences, 3(2), 155–162. doi:10.1155/S1173912699000085
  • Kot, M. (2001). Elements of mathematical ecology. Cambridge: Cambridge University Press.
  • Kroeker, K. J., Sanford, E., Jellison, B. M., & Gaylord, B. (2014). Predicting the effects of ocean acidification on predator-prey interactions: A conceptual framework based on coastal molluscs. The Biological Bulletin, 226(3), 211–222. doi:10.1086/BBLv226n3p211
  • Kumar, S., Chauhan, R. P., Osman, M. S., & Mohiuddine, S. A. (2021). A study on fractional HIV-AIDs transmission model with awareness effect. Mathematical Methods in the Applied Sciences.
  • Kumar, S., Kumar, R., Osman, M. S., & Samet, B. (2021). A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials. Numerical Methods for Partial Differential Equations, 37(2), 1250–1268. doi:10.1002/num.22577
  • Lotka, A. J. (1925). Elements of physical biology. Philadelphia: Williams and Wilkins.
  • Maayah, B., Yousef, F., Arqub, O. A., Momani, S., & Alsaedi, A. (2019). Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in Hilbert space with error analysis. Filomat, 33(12), 3845–3853. doi:10.2298/FIL1912845M
  • Momani, S., Arqub, O. A., Maayah, B., Yousef, F., & Alsaedi, A. (2018). A reliable algorithm for solving linear and nonlinear Schrödinger equations. Applied and Computational Mathematics, 17(2), 151–160.
  • Rilov, G. (2009). Predator–prey interactions of marine invaders. In Biological invasions in marine ecosystems (pp. 261–285). Berlin, Heidelberg: Springer.
  • Volterra, V. (1926). Fluctuations in the abundance of a species considered mathematically. Nature, 118(2972), 558–560. doi:10.1038/118558a0
  • Wang, Z., Xie, Y., Lu, J., & Li, Y. (2019). Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition. Applied Mathematics and Computation, 347, 360–369. doi:10.1016/j.amc.2018.11.016
  • Yousef, F., Alkam, O., & Saker, I. (2020). The dynamics of new motion styles in the time-dependent four-body problem: Weaving periodic solutions. The European Physical Journal Plus, 135(9), 742. doi:10.1140/epjp/s13360-020-00774-1
  • Yousef, F., Alquran, M., Jaradat, I., Momani, S., & Baleanu, D. (2019). Ternary-fractional differential transform schema: Theory and application. Advances in Continuous and Discrete Models, (2019), 197. doi:10.1186/s13662-019-2137-x
  • Yousef, F., Alquran, M., Jaradat, I., Momani, S., & Baleanu, D. (2019). New fractional analytical study of three-dimensional evolution equation equipped with three memory indices. Journal of Computtional and Nonlinear Dynamics, 14(11), 111008. doi:10.1115/1.4044585
  • Yousef, F., Semmar, B., & Al Nasr, K. (2022). Dynamics and simulations of discretized Caputo-conformable fractional-order Lotka–Volterra models. Nonlinear Engineering, 11(1), 100–111. doi:10.1515/nleng-2022-0013