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Engineering with Computers
Erschienen in: Engineering with Computers 1/2020

12.01.2019 | Original Article

Turing models in the biological pattern formation through spectral meshless radial point interpolation approach

verfasst von: Elyas Shivanian, Ahmad Jafarabadi

Erschienen in: Engineering with Computers | Ausgabe 1/2020

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Abstract

In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, to eliminate the nonlinearity, a simple predictor–corrector (P–C) scheme is performed. The effect of parameters and conditions are studied by considering the well-known Schnakenberg model.
Vorheriger Artikel 3D prediction of tunneling-induced ground movements based on a hybrid ANN and empirical methods
Nächster Artikel The use of new intelligent techniques in designing retaining walls

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Literatur
1.
Zhu J, Zhang Y-T, Newman SA, Alber M (2009) Application of discontinuous Galerkin methods for reaction-diffusion systems in developmental biology. J Sci Comput 40(1–3):391–418MathSciNetMATHCrossRef
2.
3.
Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetik 12(1):30–39MATHCrossRef
4.
Prigogine I, Lefever R (1968) Symmetry breaking instabilities in dissipative systems. II. J Chem Phys 48(4):1695–1700CrossRef
5.
Schnakenberg J (1979) Simple chemical reaction systems with limit cycle behaviour. J Theor Biol 81(3):389–400MathSciNetCrossRef
6.
Thomas D (1975) Artificial enzyme membranes, transport, memory, and oscillatory phenomena. In: Thomas D, Kernevez JP (eds) Analysis and control of immobilized enzyme systems. Springer, Berlin, Heidelberg, New York, pp 115–150
7.
Gray P, Scott SK (1983) Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability. Chem Eng Sci 38(1):29–43CrossRef
8.
Gray P, Scott SK (1984) Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A+ 2B\(\rightarrow\) 3B; B\(\rightarrow\) C. Chem Eng Sci 39(6):1087–1097CrossRef
9.
Aragón JL, Torres M, Gil D, Barrio RA, Maini PK (2002) Turing patterns with pentagonal symmetry. Phys Rev E 65(5):051913MathSciNetCrossRef
10.
Aragón JL, Varea C, Barrio RA, Maini PK (1998) Spatial patterning in modified turing systems: application to pigmentation patterns on marine fish. Forma 13(3):213–221
11.
Barrio RA, Varea C, Aragón JL, Maini PK (1999) A two-dimensional numerical study of spatial pattern formation in interacting turing systems. Bull Math Biol 61(3):483–505MATHCrossRef
12.
Barrio RA, Maini PK, Aragón JL, Torres M (2002) Size-dependent symmetry breaking in models for morphogenesis. Phys D Nonlinear Phenom 168:61–72MathSciNetMATHCrossRef
13.
Shirzadi A, Sladek V, Sladek J (2013) A local integral equation formulation to solve coupled nonlinear reaction-diffusion equations by using moving least square approximation. Eng Anal Bound Elem 37(1):8–14MathSciNetMATHCrossRef
14.
15.
Hundsdorfer W, Verwer JG (2013) Numerical solution of time-dependent advection-diffusion-reaction equations. Springer Science & Business Media, New YorkMATH
16.
17.
Dehghan M, Abbaszadeh M, Mohebbi A (2016) The use of element free Galerkin method based on moving Kriging and radial point interpolation techniques for solving some types of Turing models. Eng Anal Bound Elem 62:93–111MathSciNetMATHCrossRef
18.
Twizell EH, Gumel AB, Cao Q (1999) A second-order scheme for the Brusselator reaction–diffusion system. J Math Chem 26(4):297–316MathSciNetMATHCrossRef
19.
Madzvamuse A, Maini PK (2007) Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains. J Comput Phys 225(1):100–119MathSciNetMATHCrossRef
20.
Shakeri F, Dehghan M (2011) The finite volume spectral element method to solve turing models in the biological pattern formation. Comput Math Appl 62(12):4322–4336MathSciNetMATHCrossRef
21.
Madzvamuse A, Chung AHW (2014) Fully implicit time-stepping schemes and non-linear solvers for systems of reaction–diffusion equations. Appl Math Comput 244:361–374MathSciNetMATH
22.
Sladek V, Sladek J, Shirzadi A (2015) The local integral equation method for pattern formation simulations in reaction–diffusion systems. Eng Anal Bound Elem 50:329–340MathSciNetMATHCrossRef
23.
Campagna R, Cuomo S, Giannino F, Severino G, Toraldo G (2018) A semi-automatic numerical algorithm for turing patterns formation in a reaction-diffusion model. IEEE Access 6:4720–4724CrossRef
24.
Campagna R, Brancaccio M, Cuomo S, Mazzoleni S, Russo L, Siettos K, Giannino F (2017) Numerical approaches to model perturbation fire in turing pattern formations. In: AIP conference proceedings, vol 1906, p 100011. AIP Publishing
25.
Burrage K, Hale N, Kay D (2012) An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. SIAM J Sci Comput 34(4):A2145–A2172MathSciNetMATHCrossRef
26.
Zhuang P, Liu F, Turner I, YuanTong G (2014) Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation. Appl Math Model 38(15):3860–3870MathSciNetMATHCrossRef
27.
Katsikadelis JT (2011) The BEM for numerical solution of partial fractional differential equations. Comput Math Appl 62(3):891–901MathSciNetMATHCrossRef
28.
Fasshauer GE (2007) Meshfree approximation methods with MATLAB, vol 6. World Scientific, SingaporeMATHCrossRef
29.
Fasshauer GE, Zhang JG (2007) On choosing optimal shape parameters for RBF approximation. Numer Algorithms 45(1–4):345–368MathSciNetMATHCrossRef
30.
Shivanian E, Jafarabadi A (2017) Numerical solution of two-dimensional inverse force function in the wave equation with nonlocal boundary conditions. Inverse Probl Sci Eng 25(12):1743–1767MathSciNetMATHCrossRef
31.
Shivanian E, Jafarabadi A (2018) An inverse problem of identifying the control function in two and three-dimensional parabolic equations through the spectral meshless radial point interpolation. Appl Math Comput 325:82–101MathSciNetMATH
32.
Shivanian E, Jafarabadi A (2017) Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general-shaped domains. Numer Methods Partial Differ Equ 33(4):1043–1069MATHCrossRef
33.
Jafarabadi A, Shivanian E (2018) Numerical simulation of nonlinear coupled Burgers equation through meshless radial point interpolation method. Eng Anal Bound Elem 95:187–199MathSciNetMATHCrossRef
34.
Wendland H (1998) Error estimates for interpolation by compactly supported radial basis functions of minimal degree. J Approx Theory 93(2):258–272MathSciNetMATHCrossRef
35.
Shivanian E (2015) A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms. Eng Anal Bound Elem 54:1–12MathSciNetMATHCrossRef
36.
Shivanian E, Jafarabadi A (2017) Inverse Cauchy problem of annulus domains in the framework of spectral meshless radial point interpolation. Eng Comput 33(3):431–442MATHCrossRef
37.
Dehghan M, Ghesmati A (2010) Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput Phys Commun 181(4):772–786MathSciNetMATHCrossRef
Metadaten
Titel
Turing models in the biological pattern formation through spectral meshless radial point interpolation approach
verfasst von
Elyas Shivanian
Ahmad Jafarabadi
Publikationsdatum
12.01.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 1/2020
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-018-00698-6

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