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Atencia M, Joya G, Sandoval F (2005) Dynamical analysis of continuous higher-order hopfield networks for combinatorial optimization. Neural Comput 17:1802-19 [PubMed]

References and models cited by this paper

References and models that cite this paper

Abe S (1989) Theories on the Hopfield neural networks Proc IEEE Int J Conf Neural Networks 1:557-564

Abe S (1993) Global convergence and suppression of spurious states of the Hopfield neural networks IEEE Trans Circuits And Systems 40:246-257

Abe S (1996) Convergence acceleration of the Hopfield neural network by optimizing integration step sizes. IEEE Trans Syst Man Cybern B Cybern 26:194-201 [Journal] [PubMed]

Abe S, Gee AH (1995) Global convergence of the Hopfield neural network with nonzero diagonal elements IEEE Trans Circuits Systems 42:39-45

Algaba A, Merino M, Freire E, Gamero E, Rodriguez-Luis A (2003) Some results on Chuas equation near a triple-zero linear degeneracy Int J Bifur Chaos 13:583-608

Atencia MA, Joya G, Sandoval F (2003) Hopfield neural networks for parametric identification of a robotic system Proc. Engineering Application of Neural Networks Conference (EANN 2003), Malaga (Spain) :311-318

Atencia MA, Joya G, Sandoval F (2003) Spurious minima and basins of attraction in higher-order Hopfield networks Computational methods in neural modeling, Mira J:Alvarez JR, ed.

Bharitkar S, Tsuchiya K, Takefuji Y (1999) Microcode optimization with neural networks. IEEE Trans Neural Netw 10:698-703 [Journal] [PubMed]

Bronshtein I, Semendyayev K, Musiol G, Muehlig H (2004) Handbook of mathematics

Chen T, Amari SI (2001) New theorems on global convergence of some dynamical systems. Neural Netw 14:251-5 [PubMed]

Ciarlet P, Lions J (2002) Handbook of numerical analysis

Demmel J (2000) Hermitian eigenproblems Templates for the solution of algebraic eigenvalue problems: A practical guide, Bai Z:Demmel J:Dongarra J:Ruhe A:van der Vorst H, ed. pp.11

Feng J, Brown D (1998) Fixed-point attractor analysis for a class of neurodynamics Neural Comput 10:189-213

Golub GH, van_Loan CF (1996) Matrix computations

Guckenheimer J, Holmes P (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd edition.

Hirsch MW, Smale S (1974) Differential Equations, Dynamical Systems and Linear Algebra

Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci U S A 81:3088-92 [PubMed]

Hopfield JJ, Tank DW (1985) "Neural" computation of decisions in optimization problems. Biol Cybern 52:141-52 [PubMed]

Horn RA, Johnson CR (1985) Matrix analysis

Joya G, Atencia MA, Sandoval F (1997) Associating arbitrary-order energy functions to an artificial neural network: Implications concerning the resolution of optimization problems Neurocomputing 14:139-156

Joya G, Atencia MA, Sandoval F (2002) Hopfield neural networks for optimization: Study of the different dynamics Neurocomputing 43:219-237

Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10:1366-74 [Journal] [PubMed]

Matsuda S (1998) "Optimal" Hopfield network for combinatorial optimization with linear cost function. IEEE Trans Neural Netw 9:1319-30 [Journal] [PubMed]

Matsuda S (2002) Optimal neural representation of higher order for traveling salesman problems Electronics and Communications in Japan (part 2) 85:32-42

Pardalos PM, Resende MG (2002) Handbook of applied optimization

Riaza R, Zufiria PJ (2002) Discretization of implicit ODEs for singular root-finding problems J Comput Appl Math 140:695-712

Samad T, Harper P (1990) High-order Hopfield and Tank optimization networks Parallel Computing 16:287-292

Schropp J (1995) Using dynamical systems methods to solve minimization problems Appl Numer Math 18:321-335

Schropp J (2000) One-step and multistep procedures for constrained minimization problems IMA J Numer Anal 20:135-152

Sejnowski TJ (1986) Higher-order Boltzmann machines Neural networks for computing, Denker JS, ed. pp.398

Smith KA (1999) Neural networks for combinatorial optimization: A review of more than a decade of research INFORMS J Comput 11:15-34

Stuart A, Humphries A (1996) Dynamical systems and numerical analysis

Takefuji Y, Lee KC (1991) Artificial neural networks for four-coloring map problems and K-colorability problems IEEE Trans Circuits Systems 38:326-333

Tino P, Horne BG, Giles CL (2001) Attractive periodic sets in discrete-time recurrent networks (with emphasis on fixed-point stability and bifurcations in two-neuron networks). Neural Comput 13:1379-414 [PubMed]

Vidyasagar M (1995) Minimum-seeking properties of analog neural networks with multilinear objective functions IEEE Trans Auto Control 40:1359-1375

Wilson GV, Pawley GS (1988) On the stability of the Travelling Salesman Problem algorithm of Hopfield and Tank. Biol Cybern 58:63-70 [PubMed]

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