Analysis and synthesis of a class of neural networks; Linear systems operating on a closed hypercube

Journal Article · Tue Oct 31 23:00:00 EST 1989 · IEEE Transactions on Circuits and Systems (Institute of Electrical and Electronics Engineers); (USA)

DOI:https://doi.org/10.1109/31.41297· OSTI ID:7183918

Li, J H; Michel, A N; Porod, W ^[1]

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1. Dept. of Electrical and Computer Engineering, Univ. of Notre Dame, Notre Dame, IN (US)

The authors investigate the qualitative properties of a class of neural networks described by a system of first-order linear ordinary differential equations which are defined on a closed hypercube of the state space with solutions extended to the boundary of the hypercube. When solutions are located on the boundary of the hypercube, the system is the to be in saturated mode. The class of systems considered herein retain the basic structure of the Hopfield model and is easier to analyze, synthesize and implement than the Hopfield model. An efficient analysis method is developed which can be used to completely determine the set of asymptotically stable equilibrium points and the set of unstable equilibrium points. The latter set can be used to estimate the domains of attraction for the elements of the former set. The synthesis procedure which the authors previously developed is modified and applied to the present class of neural networks. The class of systems considered herein can easily be implemented in analog integrated circuits. The applicability of the present results is demonstrated by means of several examples.

• OSTI ID: 7183918
• Journal Information: IEEE Transactions on Circuits and Systems (Institute of Electrical and Electronics Engineers); (USA), Journal Name: IEEE Transactions on Circuits and Systems (Institute of Electrical and Electronics Engineers); (USA) Vol. 36:11; ISSN 0098-4094; ISSN ICSYB
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ASYMPTOTIC SOLUTIONS
COMPUTER ARCHITECTURE
COMPUTERIZED SIMULATION
COMPUTERS
DESIGN
DIFFERENTIAL EQUATIONS
ELECTRONIC CIRCUITS
EQUATIONS
HYPERCUBE COMPUTERS
INTEGRATED CIRCUITS
LINEAR PROGRAMMING
MATHEMATICAL LOGIC
MICROELECTRONIC CIRCUITS
NEURAL NETWORKS
PARALLEL PROCESSING
PROGRAMMING
SIMULATION