649
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Numerical analysis of Bazykin–Berezovskaya model

, , & ORCID Icon
Article: 2190020 | Received 06 Dec 2022, Accepted 08 Mar 2023, Published online: 22 Mar 2023

References

  • Lotka AJ. Elements of physical biology. Baltimore (MD): Williams and Wilkins; 1925.
  • Volterra V. Variazioni e fluttuazioni del numero d"Individui in specie animali conviventi. Memoire del R. Comitato talaassografico italiano, men CXXXI; 1927.
  • Lou Y, Ni W-M. Diffusion, self-diffusion and cross-diffusion. J Differ Equ. 1996;131:79–131.
  • Zafar ZUA, Shah Z, Ali N, et al. Numerical study and stability of the Lengyel Epstein chemical model with diffusion. Adv Differ Equ. 2020;2020:427.
  • Zafar ZUA, Ali N, Inc M, et al. Mathematical modeling of corona virus (COVID-19) and stability analysis. Comput Methods Biomech Biomed Eng. 2022:1–20. DOI:10.1080/10255842.2022.2109020.
  • Zafar ZUA, Hussain MT, Inc M, et al. Fractional order dynamics of human papillomavirus. Res Phys. 2022;34:Article ID 105281.
  • Zafar ZUA, Ali N, Baleanu D. Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats. Chaos Solitons Fract. 2021;151:Article ID 111261.
  • Allee WC, Bowen E. Studies in animal aggregations: mass protection against colloidal silver among goldfishes. J Exp Zool. 1932;61:185–207.
  • Bazykin AD. Nonlinear dynamics of interacting populations. Singapore: World Scientific; 1998.
  • Akrami MH. Dynamical behaviours of Bazykin-Berezovskayamodel with fractional-order and its discretization. Comput Methods Differ Equ. 2021;9(4):1013–1027. DOI:10.22034/cmde.2020.30802.1460.
  • Ben Saad A, Boubaker O. On bifurcation analysis of the predator-prey BB-model with weak allee effect. In: 16th Int. Conf. Sciences and Techniques of Automatic Control and Computer Engineering (STA). IEEE; 2015. p. 19–23.
  • Bashkirtseva l, Ryashko L. Noise-induced extinction in Bazykin-Berezovskaya population model. Eur Phys J B. 2016;89:165.
  • Ben Saad A, Boubaker O. A new fractional-order predator-prey system with Allee effect. In: Azar, et al., editor. Fractional order control and synchronization of chaotic systems. Studies in computational intelligence. Vol. 688. Springer; 2017. p. 857–877.
  • He Z, Lai X. Bifurcation and chaotic behavior of a discrete-time predator-prey system. Nonlinear Anal RWA. 2011;12:403–417.
  • Jing Z, Yang J. Bifurcation and chaos in discretetime predator-prey system. Chaos Soliton Fract. 2006;27:259–277.
  • Liu X, Xiao D. Complex dynamic behaviors of a discrete-time predator-prey system. Chaos Soliton Fract. 2007;32:80–94.
  • Li B, He Z. Bifurcations and chaos in a twodimensional discrete Hindmarsh-Rose model. Nonlinear Dyn. 2014;76(1):697–715.
  • Yuan LG, Yang QG. Bifurcation, invariant curve and hybrid control in a discrete-time predator-prey system. Appl Math Model. 2015;39(8):2345–2362.
  • Cheng L, Cao H. Bifurcation analysis of a discretetime ratio-dependent predator-prey model with Allee Effect. Commun Nonlinear Sci Numer Simulat. 2016;38:288–302.
  • Kartal S. Dynamics of a plant-herbivore model with differential-difference equations. Cogent Math. 2016;3(1):Article ID 1136198.
  • Chen B, Chen J. Complex dynamic behaviors of a discrete predator-prey model with stage structure and harvesting. Int J Biomath. 2017;10(1):Article ID 1750013.
  • Pal. S. K. Sasmal S, Pal N. Chaos control in a discrete-time predator-prey model with weak Allee effect. Int J Biomath. 2018;11(7):Article ID 1850089.
  • Kartal S, Fuat G. Global behaviour of a predator-prey like model with piecewise constant arguments. J Biol Dyn. 2015;9:159–171.
  • Din Q. Controlling chaos in a discrete-time prey. predator model with Allee effects. Int J Dyn Control. 2018;6(2):858–872.
  • Elabbasy EM, Elsadany AA, Zhang Y. Bifurcation analysis and chaos in a discrete reduced Lorenz system. Appl Math Comput. 2014;228:184–194.
  • Atabaigi A, Akrami MH. Dynamics and bifurcations of a hostparasite model. Int J Biomath. 2017;10(6):Article ID 1750089.
  • Salman SM, Yousef AM, Elsadany AA. Stability. bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response. Chaos Soliton Fract. 2016;93:20–31.
  • Isik S. A study of stability and bifurcation analysis in discrete-time predatorprey system involving the Allee effect. Int J Biomath. 2019;12(1):Article ID 1950011.
  • Din Q. Complexity and chaos control in a discretetime prey-predator model. Commun Nonlinear Sci Numer Simul. 2017;49:113–134.
  • Abd-Elhameed WM, Machado JAT, Youssri YH. Hypergeometric fractional derivative formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations. Int J Nonlinear Sci Numer Simul. 2022;23(7-8):1253–1268. DOI:10.1515/ijnsns-2020-0124.
  • Hafez RM, Youssri YH. Shifed Gegenbaur-Gauss collocation method for solving fractional-differential equations with proportional delays. Kragujevac J Math. 2022;46(6):981–996.
  • Youssri YH, Abd-Elhameed WM, Ahmad HM. New fractional derivative expression of the shifted third kind Chebyshev polynomials: application to a type of nonlinear fractional pantograph differential equations. J Funct Spaces. 2022;2022:Article ID 3966135. DOI:10.1155/2022/3966135.
  • Youssri YH, Abd-Elhameed WM, Mohamed AS, et al. Generalized lucas polynomial sequence treatment of fractional pantograph differential equation. Int J Appl Comput Math. 2021;7(27):1253–1268. DOI:10.1007/s40819-021-00958-y.
  • Tunç C. Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments. Electron J Qual Theory Differ Equ. 2010;1:12 pp. DOI:10.14232/ejqtde.2010.1.1.
  • Tunç C. Stability and bounded of solutions to non-autonomous delay differential equations of third order. Nonlinear Dyn. 2010;62:945–953. https://doi.org/10.1007/s11071-010-9776-5.
  • Tunç C. Stability to vector Liénard equation with constant deviating argument. Nonlinear Dyn. 2013;73:1245–1251. DOI:10.1007/s11071-012-0704-8.
  • Tunc C. Qualitative properties in nonlinear Volterra integro-differential equations with delay. J Taibah Univ Sci. 2017;1(2):309–314. DOI:10.1016/j.jtusci.2015.12.009.
  • Tunc C, Dinç Y. Qualitative properties of certain non-linear differential systems of second order. J Taibah Univ Sci. 2017;11(2):359–366. DOI:10.1016/j.jtusci.2016.05.002.
  • Tunç C, Tunç O. On the asymptotic stability of solutions of stochastic differential delay equations of second order. J Taibah Univ Sci 2019;13(1):875–882. DOI:10.1080/16583655.2019.1595359.
  • Tunç C, Tunç O. A note on certain qualitative properties of a second order linear differential system. Appl Math Inf Sci. 2015;9(2):953–956. DOI:10.12785/amis/090245.
  • Tunç C, Tunç, O. On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order. J Adv Res. 2016;7(1):165–168. DOI:10.1016/j.jare.2015.04.005.
  • Tunç C, Tunç O. A note on the stability and boundedness of solutions to non-linear differential systems of second order. J Assoc Arab Univ Basic Appl Sci. 2017;24:169–175. DOI:10.1016/j.jaubas.2016.12.004.
  • Lou Y, Ni WM. Diffusion, self-diffusion and cross-diffusion. J Differ Equ. 1996;131:79–131.