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Stochastic Neural Network Model: Part 2

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Stochastic Neural Network Model: Part 2

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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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 Distributions Compare 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 Iteration Pts. on the return map Slide 9 of 17
  9. 9. Logistic Equation: First Return Map f(n+1) f(n) Slide 10 of 17
  10. 10. Logistic Equation: Return Map 2 f(n+2) f(n) Slide 11 of 17
  11. 11. Logistic Map: Return Map 3 f(n+3) f(n) Slide 12 of 17
  12. 12. Logistic Equation: Return Map 4 f(n+4) f(n) Slide 13 of 17
  13. 13. Logistic Equation: Return Map 5 f(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. Sources Physical Review E pre.aps.org Nature nature.com Chaos: the making of a new science James Gleick Python programming language python.org MATLAB® computing language mathworks.in/products/matlab Univ. of Yale online resources on chaos classes.yale.edu/fractals/chaos/welcome.html California State Univ. East Bay Hayward Statistics Dept. online resources sci.csueastbay.edu/statistics/Resources/Essays/PoisExp.htm Slide 17 of 17

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