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Abstract: In this paper, we investigates a simple discrete-time model, which produces the winner-take-all competition. The local and global stability of the model are both proven theoretically. Simulations are conducted for both the static competition and the dynamic competition scenarios. The numerical results validate the theoretical results and demonstrate the effectiveness of the model in generating winner-take-all competition. [Copyright &y& Elsevier]

Abstract The star chromatic index of a multigraph G , denoted χ s ′ (G) , is the minimum number of colors needed to properly color the edges of G such that no path or cycle of length four is bi-colored. A multigraph G is star k -edge-colorable if χ s ′ (G) ≤ k. Dvořák et al. (2013) proved that every subcubic multigraph is star 7-edge-colorable. They conjectured in the same paper that every subcubic multigraph should be star 6-edge-colorable. In this paper, we consider this problem in a more general setting, we investigate star list edge coloring of general graph G and obtain an upper bound for the choice number of star edge coloring of graphs, namely, we proved that χ s l ′ ≤ ⌈ 2 Δ 3 2 (1 Δ + 2) 1 2 + 2 Δ ⌉. [ABSTRACT FROM AUTHOR]