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Transactions ID Number: 53-454
Full Name: Guang Zhang
Position: Professor
Age: ON
Sex: Male
Address: Tianjin University of Commerce, Tianjin
Country: CHINA
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Title of the Paper: Effect of random initial value for pattern formation
Authors as they appear in the Paper: Li Xu, Guang Zhang, Jun-fen Ren
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Number of paper pages: 10
Abstract: Patterns observed in natural phenomena may be modeled as a combination of both fluctuations of system parameters and variation of the initial conditions. In this paper, a two-dimensional Logistic coupled map lattice will be recurred to present mathematical mechanism of the effect of random initial values for pattern development. In fact, the asymptotic behavior of solutions is determinted by the corresponding eigenvectors and the eigenvalues of a discrete Laplace operator. That is, any random intial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact.
Keywords: Logistic coupled map lattice; random initial values; pattern formation; eigenvector; discrete Laplace operator
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