Design of Complex-valued Hopfield Associative Memory Based on Prespecified Attractive Domain

This paper proposes a connection weighting scheme of a complex-valued Hopfield neural network for associative memory constrained by given attractive domain. Both equilibrium conditions and stability analysis results are used in the synthesis procedure. We solve the equilibrium equation by singular value decomposition technique and obtain a general solution of the connection weight matrix with a free sub-matrix. Such general solution and the parameter matrix corresponding to the given attractive domain are contained in the inequations which are derived from stability analysis and can be represented as linear matrix inequations (LMIs). The connection weighting solution of such LMIs can guarantee stability and attractability of the network simultaneously. A simulation example of a 3-dimension complex-valued Hopfield neural network shows the proposed synthesis method. The simulation results demonstrate the attractive ability of two complex-valued vectors in the prespecified attractive domain.