Araştırma Makalesi
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Yıl 2022, Cilt: 4 Sayı: 1, 15 - 30, 30.08.2022

Serap Mutlu Metin Basarır

https://doi.org/10.47086/pims.1120339

Öz

Kaynakça

  • [1] Ahmed, E., El-Sayed, A., El-Saka, H.: Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. J.Math. Anal. Appl. 325, 542–553 (2007)
  • [2] Aizerman, M., Gantmacher, F.: Absolute Stability of Regulator Systems. Holden-Day, San Francisco (1964)
  • [3] Chen, J., Zeng, Z., Jiang, P.: Global Mittag-Leffler stability and synchronization of memristor-based fractional-orderneural networks. Neural Netw. 51, 1–8 (2014)
  • [4] Du, M., Wang, Z., Hu, H.: Measuring memory with the order of fractional derivative. Sci. Rep. 3, 3431 (2013)
  • [5] Elettreby, M.F.: Two-prey one-predator model. Chaos Solitons Fractals 39 (5), 2018–2027, (2009)
  • [6] Garrappa, R.: Numerical solution of fractional differential equations: a survey and a software tutorial. Mathematics 6 (2), 1–16 (2018)
  • [7] Ghanabri, B., Djilali, S.: Mathematical and numerical analysis of a three-species predator– prey model with herd behavior and time-fractional-order derivative. Math. Methods Appl. Sci.(2019). https://doi.org/10.1002/mma.5999
  • [8] Ghanabri, B., Djilali, S.:Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative. Advances in difference Equations. 2021:235, 1-19 (2021).
  • [9] Holling, C.S.: The functional response of invertebrate predator to prey density. Mem. Entomol. Soc. Can. 45, 3–60 (1965)
  • [10] Huang, Y., Chen, F., Li, Z.: Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge. Appl.Math. Comput. 182, 672-683 (2006)
  • [11] Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Application of Fractional Differential Equations. Elsevier, New York (2006).
  • [12] Lefschetz, S.: Stability of Nonlinear Control Systems. Academic Press, New York (1965)
  • [13] Li, H., Muhammedhaji, A., Zhang, L., Teng, Z.: Stability analysis of a fractional-order predator–prey model incorporating a constant prey refuge and feedback control. 2018:325, 1-12 (2018).
  • [14] Ma, Z., Li, W., Zhao, Y., Wang, W., Zhang, H., Li, Z.: Effects of prey refuges on a predatorprey model with a class o functional responses: the role of refuges. Math. Biosci. 218 (2), 73–79 (2009)
  • [15] Ma, Z.: The research of predator–prey models incorporating prey refuges. Ph.D. Thesis, Lanzhou University, P.R. China (2010)
  • [16] Matouk, A.: Chaos, feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit. Commun. Nonlinear Sci. Numer. Simul. 16, 975– 986 (2011)
  • [17] Mondal, S., Lahiri, A., Bairagi, N.: Analysis of a fractional order eco-epidemiological model with prey infection and type 2 functional response. Math. Methods Appl. Sci. 40, 6776–6789 (2017)
  • [18] Moustafa, M., Mohd, M., Ismail, A., Abdullah, F.: Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge. Chaos Solitons Fractals 100, 1–13 (2018)
  • [19] Persson, L.: Behavioral response to predators reverses the outcome of competition between prey species. Behav. Ecol. Sociobiol. 28, 101–105 (1991)
  • [20] Petras, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Higher Education Press, Beijing. (2011)
  • [21] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

STABILITY ANALYSIS OF TWO PREDATORS-ONE PREY MODEL WITH FEEDBACK CONTROL AND TIME FRACTIONAL DERIVATIVE

Yıl 2022, Cilt: 4 Sayı: 1, 15 - 30, 30.08.2022

Serap Mutlu Metin Basarır

https://doi.org/10.47086/pims.1120339

Öz

The interaction between prey and predator is one of the most
fundamental processes in ecology. In this paper, we first consider the system
incorporating a feedback control and we discuss the dynamic behavior of preypredator
interaction model that includes two competitive predators and one prey with a generalized interaction functional. The primary resumption in the model construction is the effects of feedback control and the competition between two predators on the only prey which gives a strong implication of the real-world situation. By analyzing characteristic equations, we carry out detailed discussion with respect to stability of equilibrium points of the considered model. Further, we investigate the impact of the memory measured
by fractional time derivative on the temporal behavior.

Anahtar Kelimeler

Predator-prey model Predator-prey model; Stability; Fractional-order; Feedback control; Population dynamics; Predator competition Predator-prey model; Stability; Fractional-order; Feedback control; Population dynamics; Predator competition

Kaynakça

  • [1] Ahmed, E., El-Sayed, A., El-Saka, H.: Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. J.Math. Anal. Appl. 325, 542–553 (2007)
  • [2] Aizerman, M., Gantmacher, F.: Absolute Stability of Regulator Systems. Holden-Day, San Francisco (1964)
  • [3] Chen, J., Zeng, Z., Jiang, P.: Global Mittag-Leffler stability and synchronization of memristor-based fractional-orderneural networks. Neural Netw. 51, 1–8 (2014)
  • [4] Du, M., Wang, Z., Hu, H.: Measuring memory with the order of fractional derivative. Sci. Rep. 3, 3431 (2013)
  • [5] Elettreby, M.F.: Two-prey one-predator model. Chaos Solitons Fractals 39 (5), 2018–2027, (2009)
  • [6] Garrappa, R.: Numerical solution of fractional differential equations: a survey and a software tutorial. Mathematics 6 (2), 1–16 (2018)
  • [7] Ghanabri, B., Djilali, S.: Mathematical and numerical analysis of a three-species predator– prey model with herd behavior and time-fractional-order derivative. Math. Methods Appl. Sci.(2019). https://doi.org/10.1002/mma.5999
  • [8] Ghanabri, B., Djilali, S.:Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative. Advances in difference Equations. 2021:235, 1-19 (2021).
  • [9] Holling, C.S.: The functional response of invertebrate predator to prey density. Mem. Entomol. Soc. Can. 45, 3–60 (1965)
  • [10] Huang, Y., Chen, F., Li, Z.: Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge. Appl.Math. Comput. 182, 672-683 (2006)
  • [11] Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Application of Fractional Differential Equations. Elsevier, New York (2006).
  • [12] Lefschetz, S.: Stability of Nonlinear Control Systems. Academic Press, New York (1965)
  • [13] Li, H., Muhammedhaji, A., Zhang, L., Teng, Z.: Stability analysis of a fractional-order predator–prey model incorporating a constant prey refuge and feedback control. 2018:325, 1-12 (2018).
  • [14] Ma, Z., Li, W., Zhao, Y., Wang, W., Zhang, H., Li, Z.: Effects of prey refuges on a predatorprey model with a class o functional responses: the role of refuges. Math. Biosci. 218 (2), 73–79 (2009)
  • [15] Ma, Z.: The research of predator–prey models incorporating prey refuges. Ph.D. Thesis, Lanzhou University, P.R. China (2010)
  • [16] Matouk, A.: Chaos, feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit. Commun. Nonlinear Sci. Numer. Simul. 16, 975– 986 (2011)
  • [17] Mondal, S., Lahiri, A., Bairagi, N.: Analysis of a fractional order eco-epidemiological model with prey infection and type 2 functional response. Math. Methods Appl. Sci. 40, 6776–6789 (2017)
  • [18] Moustafa, M., Mohd, M., Ismail, A., Abdullah, F.: Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge. Chaos Solitons Fractals 100, 1–13 (2018)
  • [19] Persson, L.: Behavioral response to predators reverses the outcome of competition between prey species. Behav. Ecol. Sociobiol. 28, 101–105 (1991)
  • [20] Petras, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Higher Education Press, Beijing. (2011)
  • [21] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yazılım Mühendisliği (Diğer)
Bölüm Articles
Yazarlar

Serap Mutlu 0000-0001-8984-9681

Metin Basarır 0000-0002-4341-4399

Yayımlanma Tarihi 30 Ağustos 2022
Kabul Tarihi 30 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 4 Sayı: 1

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