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Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 53-463
Full Name: Guang Zhang
Position: Professor
Age: ON
Sex: Male
Address: Tianjin University of Commerce, BeiChen, Tianjin
Country: CHINA
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E-mail address: qd_gzhang@126.com
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Title of the Paper: Turing instability and wave patterns for a symmetric discrete
Authors as they appear in the Paper: Yu-tao Han, Bo Han, Lu Zhang, Li Xu, Mei-feng Li, Guang Zhang
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Number of paper pages: 10
Abstract: In this paper, Turing instability of a symmetric discrete competitive Lotka-Volterra system is considered. To this end, conditions for producing Turing instability of a general discrete system is attained and this conclusion is applied to the discrete competition Lotka-Volterra system. Then a series of numerical simulations of the discrete model are performed with different parameters. Results show that the discrete competitive Lotka-Volterra system can generate a large variety of wave patterns. Particularly, the diffusion coefficients can be equivalent, that is, there is neither "activator" nor "inhibitor". Similar results can not be obtained for the corresponding continuous models. On the other hand, the number of the eigenvalues is illuminated by calculation and the unstable spaces can be clearly expressed. Thus, the Turing mechanism is also explained.
Keywords: Turing instability; Diffusion; Discrete system; Eigenvalue; Lotka-Volterra system; Wave pattern
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