Numerical Simulation of Reaction-Diffusion Systems of Turing Pattern Formation
Affiliation(s)
School of Mathematics and Physics, North China Electrical Power University, Baoding, China.
School of Mathematics and Physics, North China Electrical Power University, Baoding, China.
ABSTRACT
Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.
Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.
Cite this paper
Gu, G. and Peng, H. (2015) Numerical Simulation of Reaction-Diffusion Systems of Turing Pattern Formation. International Journal of Modern Nonlinear Theory and Application, 4, 215-225. doi: 10.4236/ijmnta.2015.44016.
Gu, G. and Peng, H. (2015) Numerical Simulation of Reaction-Diffusion Systems of Turing Pattern Formation. International Journal of Modern Nonlinear Theory and Application, 4, 215-225. doi: 10.4236/ijmnta.2015.44016.
References
[1] Ouyang, Q. (2010) Nonlinear Science and Pattern Dynamics. Peking University Press, Beijing. [2] Ouyang, Q. (2000) Reaction Diffusion System Pattern Dynamics. Shanghai Science and Technology Education Press, Shanghai. [3] Liu, P.P. (2009) A Ratio Dependent Predator-Prey Model of Spatial Pattern Formation Research. Mathematics in Practice and Theory, 39, 114-119. [4] Wang, Y., Cao, J.D., Sun, G.-Q. and Li, J. (2014) Effect of Time Delay on Pattern Dynamics in a Spatial Epidemic Model. Physica A: Statistical Mechanics and Its Applications, 412, 137-148.
http://dx.doi.org/10.1016/j.physa.2014.06.038 [5] Parshad, R.D., Kumari, N., Kasimov, A.R. and Abderrahmane, H.A. (2013) Turing Patterns and Long-Time Behavior in a Three-Species Food-Chain Model. Mathematical Biosciences, 254, 83-102.
http://dx.doi.org/10.1016/j.mbs.2014.06.007 [6] Liu, S.H. and Gu, Y.X. (2012) Coupled Reaction-Diffusion System in the Superlattice Pattern. Hebei University (Natural Science Edition), 32, 597-601. [7] Du, Y.-K. and Xu, R. (2014) Pattern Formation in Two Classes of SIR Epidemic Models with Spatial Diffusion. Chinese Journal of Engineering Mathematics, 31, 454-462. [8] Li, X.Z., Bai, Z.G., Li, Y., Zhao, K. and He, Y.F. (2013) Double Nonlinear Coupling Reaction-Diffusion Systems in Complex Turing Patterns. Chinese Journal of Physics, 62, 220503-1 -220503-7.
[1] Ouyang, Q. (2010) Nonlinear Science and Pattern Dynamics. Peking University Press, Beijing. [2] Ouyang, Q. (2000) Reaction Diffusion System Pattern Dynamics. Shanghai Science and Technology Education Press, Shanghai. [3] Liu, P.P. (2009) A Ratio Dependent Predator-Prey Model of Spatial Pattern Formation Research. Mathematics in Practice and Theory, 39, 114-119. [4] Wang, Y., Cao, J.D., Sun, G.-Q. and Li, J. (2014) Effect of Time Delay on Pattern Dynamics in a Spatial Epidemic Model. Physica A: Statistical Mechanics and Its Applications, 412, 137-148.
http://dx.doi.org/10.1016/j.physa.2014.06.038 [5] Parshad, R.D., Kumari, N., Kasimov, A.R. and Abderrahmane, H.A. (2013) Turing Patterns and Long-Time Behavior in a Three-Species Food-Chain Model. Mathematical Biosciences, 254, 83-102.
http://dx.doi.org/10.1016/j.mbs.2014.06.007 [6] Liu, S.H. and Gu, Y.X. (2012) Coupled Reaction-Diffusion System in the Superlattice Pattern. Hebei University (Natural Science Edition), 32, 597-601. [7] Du, Y.-K. and Xu, R. (2014) Pattern Formation in Two Classes of SIR Epidemic Models with Spatial Diffusion. Chinese Journal of Engineering Mathematics, 31, 454-462. [8] Li, X.Z., Bai, Z.G., Li, Y., Zhao, K. and He, Y.F. (2013) Double Nonlinear Coupling Reaction-Diffusion Systems in Complex Turing Patterns. Chinese Journal of Physics, 62, 220503-1 -220503-7.