2009/02/23 by Zekeriya Uykan, Uykan, Zekeriya
Computer Science · Engineering · Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Matrix Theory and Algorithms #Neural Networks Stability and Synchronization #Optical Network Technologies #Statistics and Probability (physics.data-an) #physics.data-an
paper · pdf · doi:10.48550/arxiv.0902.3841
7 figures, submitted to IEEE Trans. on Circuits and Systems 1 (TCAS1) in Sep 2009
openalex publication_date 2009/02/23 · arxiv created 2009/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present and analyse two Hopfield-like nonlinear networks, in continuous-time and discrete-time respectively. The proposed network is based on an autonomous linear system with a symmetric weight matrix, which is designed to be unstable, and a nonlinear function stabilizing the whole network thanks to a manipulated state variable called``ultimate SIR''. This variable is observed to be equal to the traditional Signal-to-Interference Ratio (SIR) definition in telecommunications engineering. The underlying linear system of the proposed continuous-time network is \mathbf x = \mathbf B \mathbf x where \bf B is a real symmetric matrix whose diagonal elements are fixed to a constant. The nonlinear function, on the other hand, is based on the defined system variables called ``SIR''s. We also show that the ``SIR''s of all the states converge to a constant value, called ``system-specific Ultimate SIR''; which is equal to \fracrλmax where r is the diagonal element of matrix \bf B and λmax is the maximum (positive) eigenvalue of diagonally-zero matrix (\bf B - r\bf I), where \bf I denotes the identity matrix. The same result is obtained in its discrete-time version as well. Computer simulations for binary associative memory design problem show the effectiveness of the proposed network as compared to the traditional Hopfield Networks.