Memristor is a nonlinear resistor with variable resistance. This paper discusses dynamic properties of memristor and recurrent neural network (RNN) with memristors as connection weights. Firstly, it establishes that there exists a threshold voltage for memristor. Secondly, it presents a model for memristive recurrent neural network (MRNN) which has variable and bounded coefficients, and analyzes stability of memristive neural network by some maths tools. Thirdly, it gives a synthesis algorithm for associative memory based on memristive recurrent neural network. At last, three examples verify our results.
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