An operational matrix method to solve the Lotka-Volterra predator-prey models with discrete delays

YÜZBAŞI Ş.

CHAOS SOLITONS & FRACTALS, cilt.153, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 153
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.chaos.2021.111482
  • Dergi Adı: CHAOS SOLITONS & FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: Continuous population models, Predator-prey models, System of delay differential equations, Operational method, Residual error estimation, BIFURCATION, STABILITY, SYSTEM
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we consider the Lotka-Volterra predator-prey model with discrete delays. We apply the operational matrix method in [20] to this model which corresponds to a problem of nonlinear differential equations. The method is based on the operational matrices of the standard bases functions. In order to find the polynomial approximations of the known functions in the equation, the operational matrices are created by the least-squares method. The method converts the problem into a system of algebraic equations. By solving this system, the coefficients are determined. The approximate solutions are obtained by writing the coefficients in form of the approximate solutions. In addition, the accuracy of the approximate solution is checked and an error estimation technique is presented. The method is applied to some examples and the numerical results are reported. Numerical applications and comparisons with other methods show the efficiency of the current one. (c) 2021 Elsevier Ltd. All rights reserved.