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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3. My MATLAB Simulation Data
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4. My MATLAB Simulation Data
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5. 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

6. Analyzing the Distributions
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7. Analyzing the Distributions
Compare with a Monte Carlo simulation:
But of course, the sequence also matters.
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8. Logistic Equation: Time Series Plot
xi+1 = r xi (1-xi)
f(n)
n
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9. Logistic Equation: Graphical Iteration
Pts. on the return map
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10. Logistic Equation: First Return Map
f(n+1)
f(n)
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11. Logistic Equation: Return Map 2
f(n+2)
f(n)
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12. Logistic Map: Return Map 3
f(n+3)
f(n)
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13. Logistic Equation: Return Map 4
f(n+4)
f(n)
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14. Logistic Equation: Return Map 5
f(n+5)
f(n)
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15. Neural Network: First Return Map
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16. Determinants of Chaos
• Autocorrelation function
• Return map
• Sensitive dependence on initial conditions
• Unstable Periodic Orbits
• Response to Chaos Control and Anticontrol
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17. 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
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