Abstract
We study a neural network composed of excitable FitzHugh neurons that interact by diffusive type connections. Patterns of neural activity may be stored by a Hebbian rule. The stored patterns are recalled and given by the transient activity of the neurons after the network has been perturbed by related patterns and relaxes back to its steady state. Periodic perturbations of the network are repeated requests for computations and result in simple periodic, complex periodic, and chaotic responses and corresponding computational performances.
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Selected References
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- FITZHUGH R. Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J Gen Physiol. 1960 May;43:867–896. doi: 10.1085/jgp.43.5.867. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Fitzhugh R. Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J. 1961 Jul;1(6):445–466. doi: 10.1016/s0006-3495(61)86902-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hahn H. S., Nitzan A., Ortoleva P., Ross J. Threshold excitations, relaxation oscillations, and effect of noise in an enzyme reaction. Proc Natl Acad Sci U S A. 1974 Oct;71(10):4067–4071. doi: 10.1073/pnas.71.10.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hjelmfelt A., Ross J. Chemical implementation and thermodynamics of collective neural networks. Proc Natl Acad Sci U S A. 1992 Jan 1;89(1):388–391. doi: 10.1073/pnas.89.1.388. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hjelmfelt A., Schneider F. W., Ross J. Pattern recognition in coupled chemical kinetic systems. Science. 1993 Apr 16;260(5106):335–337. doi: 10.1126/science.260.5106.335. [DOI] [PubMed] [Google Scholar]
- Hjelmfelt A., Weinberger E. D., Ross J. Chemical implementation of finite-state machines. Proc Natl Acad Sci U S A. 1992 Jan 1;89(1):383–387. doi: 10.1073/pnas.89.1.383. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hjelmfelt A., Weinberger E. D., Ross J. Chemical implementation of neural networks and Turing machines. Proc Natl Acad Sci U S A. 1991 Dec 15;88(24):10983–10987. doi: 10.1073/pnas.88.24.10983. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hopfield J. J. Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A. 1982 Apr;79(8):2554–2558. doi: 10.1073/pnas.79.8.2554. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hopfield J. J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci U S A. 1984 May;81(10):3088–3092. doi: 10.1073/pnas.81.10.3088. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hopfield J. J., Tank D. W. Computing with neural circuits: a model. Science. 1986 Aug 8;233(4764):625–633. doi: 10.1126/science.3755256. [DOI] [PubMed] [Google Scholar]
- Sompolinsky H., Golomb D., Kleinfeld D. Global processing of visual stimuli in a neural network of coupled oscillators. Proc Natl Acad Sci U S A. 1990 Sep;87(18):7200–7204. doi: 10.1073/pnas.87.18.7200. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Sompolinsky H, Golomb D, Kleinfeld D. Cooperative dynamics in visual processing. Phys Rev A. 1991 Jun 15;43(12):6990–7011. doi: 10.1103/physreva.43.6990. [DOI] [PubMed] [Google Scholar]