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.

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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  • 1. Slide 2 of 17
  • 2. My MATLAB Simulation Data Slide 3 of 17
  • 3. My MATLAB Simulation Data Slide 4 of 17
  • 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. Analyzing the Distributions Slide 6 of 17
  • 6. Analyzing the DistributionsCompare with a Monte Carlo simulation: But of course, the sequence also matters. Slide 7 of 17
  • 7. Logistic Equation: Time Series Plot xi+1 = r xi (1-xi)f(n) n Slide 8 of 17
  • 8. Logistic Equation: Graphical IterationPts. on the return map Slide 9 of 17
  • 9. Logistic Equation: First Return Mapf(n+1) f(n) Slide 10 of 17
  • 10. Logistic Equation: Return Map 2f(n+2) f(n) Slide 11 of 17
  • 11. Logistic Map: Return Map 3f(n+3) f(n) Slide 12 of 17
  • 12. Logistic Equation: Return Map 4f(n+4) f(n) Slide 13 of 17
  • 13. Logistic Equation: Return Map 5f(n+5) f(n) Slide 14 of 17
  • 14. Neural Network: First Return Map Slide 15 of 17
  • 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. 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