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A novel transiently chaotic neuron was presented by transferring sigmoid activation function into non-monotonous activation function composed of Shannon wavelet and sigmoid. The reversed bifurcation and the maximum Lyapunov exponent of the chaotic neuron were given and the dynamic system was analyzed. Based on the neuron model, a novel transiently chaotic neural network was made and used to functions' optimization and combinational optimization problems. The simulation result of TSP proved that the novel transiently chaotic neural network is valid.