Bulletin of Mathematical Biology

, Volume 50, Issue 2, pp 143–185 | Cite as

Computational simulation of activity of cortical-like neural systems

  • F. Ventriglia


The kinetic theory of neural systems is extended to include the description of cortical-like neural structures. This fact is accomplished by the introduction of long-distance effects. Collaterally, we have the separation of the description of the excitatory activity from that of the inhibitory one. Also, the description of neural systems with a high level of activity is obtained. The modified theory is used to simulate computationally the activity of cortical-like neural systems.


Neural System External Disturbance Computational Simulation Probable Number Excitatory Neuron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amari, S. 1974. “A Method of Statistical Neurodynamics.”Kybernetik 14, 201–215.MATHMathSciNetGoogle Scholar
  2. Angel, E. and R. Bellman. 1972.Dynamic Programming and Partial Differential Equations, New York: Academic Press.Google Scholar
  3. Beurle, r. L. 1956. “Properties of a Mass of Cells Capable of Regenerating Pulses.”Phil. Trans. R. Soc. 240A, 55–94.Google Scholar
  4. Eccles, J. C. 1984. “The Cerebral Neocortex: A Theory of its Operation.” InCerebral Cortex, Vol.2, E. G. Jones and A. Peters (Eds), pp. 1–36. New York: Plenum Press.Google Scholar
  5. Enright, J. T. and A. T. Winfree. 1987. “Detecting a Phase Singularity in a Coupled Stochastic System.” InLectures on Mathematics in Life Sciences, Vol. 19, G. A. Carpenter (Ed.), pp. 121–150 Providence, RI: American Mathematical Society.Google Scholar
  6. Fisher, B. 1973. “A Neuron Field Theory: Mathematical Approach to the Problem of Large Numbers of Interacting Nerve Cells.”Bull. math. Biol. 35, 345–357.Google Scholar
  7. Griffith, J. S. 1963. “A Field Theory of Neural Nets—1. Derivation of Fields Equation.”Bull. math. Biophys. 25, 111–120.MATHMathSciNetGoogle Scholar
  8. Hubel, D. H. and T. N. Wiesel. 1972. “Laminar and Columnar Distribution of Geniculo-Cortical Fibers in the Macaque Monkey.”J. Comp. Neurol. 146, 421–450.CrossRefGoogle Scholar
  9. Hopfield, J. J. 1982. “Neural Networks and Physical Systems with Emergent Collective Computational Abilities.”Proc. natl. Acad. Sci. U.S.A. 79, 2554–2558.MathSciNetCrossRefGoogle Scholar
  10. Hopfield, J. J. and D. W. Tank. 1985. “Neural Computation of Decisions in Optimization Problems.”Biol. Cybern. 52, 141–152.MATHMathSciNetGoogle Scholar
  11. Ingber, L. 1982. “Statistical Mechanics of Neocortical Interactions.—I. Basic Formulation.”Physica 5D, 83–107.MathSciNetGoogle Scholar
  12. Mountcastle, V. B. 1978. “An Organizing Principle for Cerebral Function: The Unit Module and the Distributed System.” InThe Mindful Brain, Edelman and Mountcastle (Eds) Cambridge: MIT-Press.Google Scholar
  13. Peretto, P. and J.-J. Niez. 1986. “Stochastic Dynamics of Neural Networks.”IEEE Trans. Syst., Man, Cyber. 16, 73–83.MATHMathSciNetGoogle Scholar
  14. Rapoport, A. 1952. “Ignition Phenomena in Random Nets”.Bull. math. Biophys. 14, 35–44.MathSciNetGoogle Scholar
  15. Sbitnev, V. J. 1975. “Transport of Spikes in Statistical Neuron Ensembles. Conception of Phase Transition.”Akademia Nauk CCCP 176, 1–24 (in Russian).Google Scholar
  16. Szentagothai, J. 1975. “The ‘Module Concept’ in Cerebral Cortex Architecture.”Brain. Res. 95, 475–496.CrossRefGoogle Scholar
  17. — 1983. “The Modular Architectonic Principle of Neuronic Centers.”Rev. Physiol. Biochem. Pharmacol. 98 11–61.Google Scholar
  18. Ventriglia, F., 1974. “Kinetic Approach to Neural Systems. I.”Bull. math. Biol. 36, 534–544.CrossRefGoogle Scholar
  19. — 1983. “Kinetic Theory of Neural Systems: Study of the Two-dimensional Model.”Biol. Cybern. 46, 93–99.MATHMathSciNetCrossRefGoogle Scholar
  20. — 1987. “Kinetic Theory of Hot Neural Systems.”Cybern. and Systems 18, 147–155.MathSciNetGoogle Scholar
  21. — and P. Erdi. 1987. “Statistical Approach to the Dynamics of Cerebral Cortex: Learning Aspects.” InCybernetics and Systems: The Way Ahead, Vol. 1, J. Rose (Ed.), pp. 443–447, Lytham St. Annes, England: Thales.Google Scholar
  22. Wilson, H. R. and J. D. Cowan. 1973. “A Mathematical Theory of the Functional Dynamics of Cortical and Thalamic Nervous Tissue.”Kybernetik 13, 55–80.MATHCrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1988

Authors and Affiliations

  • F. Ventriglia
    • 1
  1. 1.Instituto di CiberneticaC.N.R.Arco Felice (NA)Italy

Personalised recommendations