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ANALYSIS OF ECOLOGICAL MODEL WITH HOLLING TYPE IV FUNCTIONAL RESPONSE

  • Ali S
  • Arifin N
  • Naji R
  • et al.
International Journal of Pure and Apllied Mathematics (2016) 106(1)
DOI: 10.12732/ijpam.v106i1.26
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Abstract

In this paper a three-species of predator-prey food chain model with Holling type IV functional response is proposed. The boundedness of the solution of the model is discussed. Stability analysis of the system is carried out. The dynamics of the predator-prey food chain model with simplified Holling type IV functional response is investigated theoretically as well as numerically.

Figures

  • Figure 1: Bifurcation diagram of system (2) for data in (23) the maxima of y as function of a1 and a1 ∈ (0.25, 0.5).
  • Figure 2: (A) 3D of system (2) chaotic attractor with data in (23) and a1 = 0.35. (B) 2D x− y plane of Fig.2(A).
  • Figure 3: (A) 3D of system (2) period doubling attractor with data in (23) and a1 = 0.27. (B) limit cycle attractor with data in (23) and a1 = 0.25.
  • Figure 4: (A) 3D of system (2) periodic with data set (23) and b1 = 0.60. (B) 3D of system (2) stable point with data set (23) and b1 = 1.20.
  • Figure 5: (A) 2D y − z plane of system (2) period doubling with data in (23) and d1 = 0.034. (B) 2D y − z plane of system (2) stable point with data in (23) and d2 = 0.053.
  • Figure 6: (A) Bifurcation diagram of system (2) for data in (23) the max. of (y) as function of a1 and d1 = 0.034 with a1 ∈ (0.25, 0.5).

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APA

Ali, S. J., Arifin, N. Md., Naji, R. K., Ismail, F., & Bachok, N. (2016). ANALYSIS OF ECOLOGICAL MODEL WITH HOLLING TYPE IV FUNCTIONAL RESPONSE. International Journal of Pure and Apllied Mathematics, 106(1). https://doi.org/10.12732/ijpam.v106i1.26

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