Interpolating MLPG method to investigate predator-prey population dynamic with complex characters

Abbaszadeh, Mostafa; Bagheri Salec, Alireza; Salman Alwan, Afaq

doi:10.22034/cmde.2024.59100.2508

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	Interpolating MLPG method to investigate predator-prey population dynamic with complex characters
Computational Methods for Differential Equations
مقاله 1، دوره 13، شماره 2، خرداد 2025، صفحه 357-372 اصل مقاله (4.29 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.59100.2508
نویسندگان
Mostafa Abbaszadeh^* ¹؛ Alireza Bagheri Salec²؛ Afaq Salman Alwan³
¹Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran.
²Department of Mathematics, Faculty of Basic Scince, University of Qom Alghadir Blvd., Qom, Iran.
³Department of Mathematics, Faculty of Basic Scince, University of Qom Alghadir Blvd., Qom, Iran.
چکیده
The predator-prey model is a pair of first-order nonlinear differential equations which are used to explain the dynamics of biological systems. These systems contain two species interacting, one as a predator and the other as prey. This work proposes a meshless local Petrov-Galerkin (MLPG) method based upon the interpolating moving least squares (IMLS) approximation, for the numerical solution of the predator-prey systems. With this aim, the space derivative is discretized by the MLPG technique in which the test and trial functions are chosen from the shape functions of IMLS approximation. Next, a semi-implicit finite difference approach is utilized to discretize the time derivative. The main aim of this work is to bring forward a flexible numerical procedure to solve predator-prey systems on complicated geometries.
تازه های تحقیق

کلیدواژه‌ها
Predator-prey model؛ Meshless local Petrov-Galerkin (MLPG) method؛ Interpolating IMLS approximation

اصل مقاله

مراجع
[1] M. Abbaszadeh and M. Dehghan, Direct meshless local Petrov-Galerkin (DMLPG) method for time-fractional fourth-order reaction–diffusion problem on complex domains, Computers & Mathematics with Applications, 79(3) (2020) 876–888. [2] S. A. Al-Bayati and L. C. Wrobel, Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method, International Journal of Numerical Methods for Heat & Fluid Flow. [3] S. N. Atluri, The Meshless Method (MLPG) for Domain and BIE Discretizations, Forsyth, GA (2004). [4] S. N. Atluri and T. Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, 2(2) (1998), 117–127. [5] R. Barreira, C. M. Elliott, and A. Madzvamuse, The surface finite element method for pattern formation on evolving biological surfaces, Journal of Mathematical Biology, 63(6) (2011), 1095–1119. [6] A. Bassett, A. L. Krause, and R. A. Van Gorder, Continuous dispersal in a model of predator–prey-subsidy population dynamics, Ecological Modelling, 354 (2017), 115–122. [7] L. A. Bueno, E. A. Divo, and A. J. Kassab, A coupled localized rbf meshless/drbem formulation for accurate modeling of incompressible fluid flows, International Journal of Computational Methods and Experimental Measurements 5(3) (2017) 359–368. [8] Q. A. Dang and M. T. Hoang, Nonstandard finite difference schemes for a general predator–prey system, Journal of Computational Science, 36 (2019), 101015. [9] A. Das, A. Khoury, E. Divo, V. Huayamave, A. Ceballos, R. Eaglin, A. Kassab, A. Payne, V. Yelundur, and H. Seigneur, Real-time thermomechanical modeling of pv cell fabrication via a pod-trained rbf interpolation network, Computer Modeling in Engineering & Sciences, 122(3) (2020), 757–777. [10] M. Dehghan and M. Abbaszadeh, Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach, Computers & Mathematics with Applications, 72(3) (2016), 427–454. [11] M. Dehghan, M. Abbaszadeh, and A. Mohebbi, The use of element free galerkin method based on moving Kriging and radial point interpolation techniques for solving some types of Turing models, Engineering Analysis with Boundary Elements, 62 (2016), 93–111. [12] M. Dehghan and N. Narimani, Approximation of continuous surface differential operators with the generalized moving least-squares (gmls) method for solving reaction–diffusion equation, Computational and Applied Mathematics, 37 (2018), 6955–6971. [13] M. Dehghan and M. Sabouri, A Legendre spectral element method on a large spatial domain to solve the predator– prey system modeling interacting populations, Applied Mathematical Modelling, 37(3) (2013), 1028–1038. [14] R. Dillon, P. Maini, and H. Othmer, Pattern formation in generalized Turing systems, Journal of Mathematical Biology, 32(4) (1994), 345–393. [15] D. T. Dimitrov and H. V. Kojouharov, Nonstandard finite-difference methods for predator–prey models with general functional response, Mathematics and Computers in Simulation, 78(1) (2008) 1–11. [16] M. Du, P. Ning, and Y. Wang, Numerical solution of a class of predator-prey systems with complex dynamics characters based on a sinc function interpolation collocation method, Complexity, 2020 (2020) 1–34. [17] G. Karamali, M. Abbaszadeh, and M. Dehghan, The smoothed particle hydrodynamics method for solving generalized variable coefficient schrodinger equation and schrodinger-boussinesq system, Computational Methods for Differential Equations, 6(2) (2018), 215–237. [18] L. J. Khaled-Abad and R. Salehi, Numerical and theoretical study of weak Galerkin finite element solutions of Turing patterns in reaction–diffusion systems, Numerical Methods for Partial Differential Equations, 37(1) (2021), 302–340. [19] D. Kumar and S. P. Chakrabarty, A predator–prey model with additional food supply to predators: dynamics and applications, Computational and Applied Mathematics, 37 (2018), 763–784. [20] D. Levy, H. A. Harrington, and R. A. Van Gorder, Role of seasonality on predator–prey–subsidy population dynamics, Journal of Theoretical Biology, 396 (2016), 163–181. [21] X. Li and Q. Wang, Analysis of the inherent instability of the interpolating moving least squares method when using improper polynomial bases, Engineering Analysis with Boundary Elements, 73 (2016), 21–34. [22] Y. Liu, Q. Cao, and W. Yang, Influence of allee effect and delay on dynamical behaviors of a predator–prey system, Computational and Applied Mathematics, 41(8) (2022), 396. [23] A. Madzvamuse, P. K. Maini, and A. J. Wathen, A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains, Journal of Scientific Computing, 24(2) (2005), 247–262. [24] P. Majumdar, B. Mondal, S. Debnath, and S. Sarkar, and U. Ghosh, Effect of fear and delay on a prey-predator model with predator harvesting, Computational and Applied Mathematics, 41(8) (2022), 357. [25] A. Mazzia, G. Pini, and F. Sartoretto, Numerical investigation on direct MLPG for 2D and 3D potential problems, Computer Modeling in Engineering & Sciences(CMES), 88(3) (2012), 183–209. [26] D. Mirzaei and R. Schaback, Direct meshless local Petrov-Galerkin (DMLPG) method: a generalized MLS approximation, Applied Numerical Mathematics, 68 (2013), 73–82. [27] D. Mirzaei, R. Schaback, and M. Dehghan, On generalized moving least squares and diffuse derivatives, IMA Journal of Numerical Analysis, 32(3) (2012), 983–1000. [28] M. Nemati, M. Shafiee, and H. Ebrahimi, A meshless technique based on the radial basis functions for solving systems of partial differential equations, Computational Methods for Differential Equations, 10(2) (2022), 526–537. [29] M. W. Ni, A. J. Kassab, and E. Divo, Automated hybrid singularity superposition and anchored grid pattern bem algorithm for the solution of inverse geometric problems, Engineering Analysis with Boundary Elements, 73 (2016), 69–78. [30] S. A. Sarra, A local radial basis function method for advection–diffusion–reaction equations on complexly shaped domains, Applied Mathematics and Computation, 218(19) (2012), 9853–9865. [31] F. Sartoretto, A. Mazzia, and G. Pini, The DMLPG meshless technique for Poisson problems, Appl Math Sci, 8(164) (2014) 8233–8250. [32] F. Shakeri and M. Dehghan, The finite volume spectral element method to solve Turing models in the biological pattern formation, Computers & Mathematics with Applications, 62(12) (2011), 4322–4336. [33] E. Shivanian, M. Hosseini, and A. Rahimi, Meshless local radial point interpolation (mlrpi) to two dimensional wave equation with neumann’s boundary conditions, Computational Methods for Differential Equations, 8(1) (2020), 155–172. [34] E. Shivanian and A. Jafarabadi, Turing models in the biological pattern formation through spectral meshless radial point interpolation approach, Engineering with Computers, 36(1) (2020), 271–282. [35] E. Shivanian and A. Jafarabadi, Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system, Computational Methods for Differential Equations, 9(2) (2021), 358–374. [36] J. Sladek, V. Sladek, and Y. Hon, Inverse heat conduction problems by meshless local Petrov-Galerkin method, Engineering Analysis with Boundary Elements 30(8) (2006), 650–661. [37] M. Tehseen Saleem and I. Ali, Numerical simulations of turing patterns in a reaction-diffusion model with the chebyshev spectral method, The European Physical Journal Plus, 133(10) (2018), 1–9. [38] A. M. Turing, The chemical basis of morphogenesis, Bulletin of Mathematical Biology, 52(1) (1990), 153–197. [39] L. Zhu and L. He, Two different approaches for parameter identification in a spatial–temporal rumor propagation model based on Turing patterns, Communications in Nonlinear Science and Numerical Simulation, 107 (2022), 106174.
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Interpolating MLPG method to investigate predator-prey population dynamic with complex characters