Stochastic Neural Network Model: Part 2

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A stochastic computer model for hippocampal brain activity exhibits behaviour earlier identified as deterministic chaos, and hence raises doubts over the techniques of identifying chaotic dynamics.

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Stochastic Neural Network Model: Part 2

  1. 1. Slide 2 of 17
  2. 2. My MATLAB Simulation Data Slide 3 of 17
  3. 3. My MATLAB Simulation Data Slide 4 of 17
  4. 4. Time evolution of the overlaps: 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 0 3 1 0 1 0 3 1 0 1 0 3 1 0 1 0 3 1 0 1 0 3 1 0 1 0 3 1 0 1 0 1 3 0 0 0 1 3 0 0 0 1 3 0 0 0 1 3 0 0 0 1 3 0 0 0 1 3 0 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 0 1 0 0 3 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 3 0 0 1 0 Slide 5 of 17
  5. 5. Analyzing the Distributions Slide 6 of 17
  6. 6. Analyzing the DistributionsCompare with a Monte Carlo simulation: But of course, the sequence also matters. Slide 7 of 17
  7. 7. Logistic Equation: Time Series Plot xi+1 = r xi (1-xi)f(n) n Slide 8 of 17
  8. 8. Logistic Equation: Graphical IterationPts. on the return map Slide 9 of 17
  9. 9. Logistic Equation: First Return Mapf(n+1) f(n) Slide 10 of 17
  10. 10. Logistic Equation: Return Map 2f(n+2) f(n) Slide 11 of 17
  11. 11. Logistic Map: Return Map 3f(n+3) f(n) Slide 12 of 17
  12. 12. Logistic Equation: Return Map 4f(n+4) f(n) Slide 13 of 17
  13. 13. Logistic Equation: Return Map 5f(n+5) f(n) Slide 14 of 17
  14. 14. Neural Network: First Return Map Slide 15 of 17
  15. 15. Determinants of Chaos• Autocorrelation function• Return map• Sensitive dependence on initial conditions• Unstable Periodic Orbits• Response to Chaos Control and Anticontrol Slide 16 of 17
  16. 16. SourcesPhysical Review Epre.aps.orgNaturenature.comChaos: the making of a new scienceJames GleickPython programming languagepython.orgMATLAB® computing languagemathworks.in/products/matlabUniv. of Yale online resources on chaosclasses.yale.edu/fractals/chaos/welcome.htmlCalifornia State Univ. East Bay Hayward Statistics Dept. online resourcessci.csueastbay.edu/statistics/Resources/Essays/PoisExp.htm Slide 17 of 17

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