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An associative memory network with hysteretic property and chaotic property synchronously are proposed. The neurons in the network have new activation function, which is composed of two Sigmoid function translated. Hysteretic response can be obtained in the neuron. The hysteretic property helps to avoid changing the state of the neuron mistakenly. The self-feedback weight is added, and the bifurcation processes, leading to chaos, can be exhibited with the parameter variation. The network based on this neuron model can be applied to resolve associative memory problems, and can get over some disadvantages in the conventional neural network, such as local minima, fault saturation and so on. Simulation results proved that the neural networks have good information processing ability.