Fall
2012
Recommended
reading:
Dynamical
Systems in Neuroscience – The Geometry of Excitability and Bursting
By
Eugene Izhikevich
ebook (available to Brown users)
HOMEWORKS Please hand in paper
copy in class on due date Matlab assignments: include
printout of code as well as figures Homework 1  Due
Wednesday September 19 Solutions Homework 2  Due Monday October 1
Solutions Homework 3  Due Wednesday October 10 Solutions Homework 4  Due Friday November 2
Solutions hw4.m Homework 5  Due Monday November 19 Solutions Homework 6  Due Wednesday December 5
Solutions 
FINAL EXAM Thursday 12/20/2012
2:00 PM Barus and Holley 160 
Coverage:
all material studied sinde midterm. No
computers or calculators of any kind allowed. 
Review Session – Wed Dec 12, 2012 
Class 37 – Fri Dec 7, 2012 
The LotkaVolterra PredatorPrey Model The
Lorenz system and its strange attractor code 
Class 36 – Wed Dec 5, 2012 
The PoincareBendixson Theorem An
ExcitatoryInhibitory NeuralNetwork Model 
Class 35 – Mon Dec 3, 2012 
The
FitzHughNagumo Model fitzhugh_nagumo.m 
Class 34 – Fri Nov 30, 2012 
Linearization
of NonLinear Systems (continued) 
Class 33 – Wed Nov 28, 2012 
Linearization
of NonLinear Systems 
Class 32 – Mon Nov 26, 2012 
Systems of NonLinear DEs: Examples (continued) Code:
First_Order_System.m 
Class 31 – Mon Nov 19, 2012 
An example of Eigenvector Analysis in Brain Science: The BrainStateinaBox (BSB) Model
(James
Anderson et al. 1977) Systems
of NonLinear DEs: Examples 
Class 30 – Fri Nov 16, 2012 
FourStep Study of Systems of Linear DEs 
Class 29 – Wed Nov 14, 2012 
Systems
of Linear DEs: Eigenvector Analysis (continued) 
Class 28 – Mon Nov 12, 2012 
Systems
of Linear DEs: Eigenvector Analysis 
Class 27 – Fri Nov 9, 2012 
Systems
of Linear DEs: Examples (continued) Code:
Linear_First_Order_System.m 
Class 26 – Wed Nov 7, 2012 
Systems
of Linear DEs: Examples 
Class 25 – Mon Nov 5, 2012 
More
examples (continued) 
Class 24 – Fri Nov 2, 2012 
NonHomogeneous
Linear Differential Equations (continued) More
examples (continued) 
Class 23 – Wed Oct 31, 2012 
NonHomogeneous
Linear Differential Equations 
Class 22 – Fri Oct 26, 2012 
Simple code – can be used
as template for HWs Firstorder
DEs with direction field (code) More complicated code,
with various functionalities 
Class 21 – Wed Oct 24, 2012 
Qualitative
Analysis of Differential Equations (continued) Separable
Differential Equations 
Class 20 – Mon Oct 22, 2012 
Introduction
to Differential Equations (continued) Nice Tutorial on
Membrane Equation (courtesy of David
Heeger) Qualitative
Analysis of Differential Equations 
Class 19 – Fri Oct 19, 2012 
Introduction
to Differential Equations (continued) 
Class 18 – Wed Oct 17, 2012 
Introduction
to Differential Equations 
Class 17 – Mon Oct 15, 2012 

MIDTERM EXAM – Sun Oct 14, 2012 Barus and Holley 141 
Coverage:
all material studied until exam. No
computers or calculators of any kind allowed. You
will not be asked to compute numerical values of complicated expressions or
expressions that involve exponentials or similar functions. Practice Midterm Exam Solutions 
Class 16 – Fri Oct 12, 2012 
Approximations Approximations (code) 
Class 15 – Wed Oct 10, 2012 
The Poisson Neuron, the Exponential distribution, and
the Poisson distribution (continued) 
Class 14 – Fri Oct 5, 2012 
The Poisson Neuron, the Exponential distribution, and
the Poisson distribution 
Class 13 – Wed Oct 3, 2012 

Class 12 – Mon Oct 1, 2012 
Covariances and related notions 
Class 11 – Fri Sept 28, 2012 
Basic Statistics for the Binomial Distribution The case of the forgetful professor 
Class 10 – Wed Sept 26, 2012 taught by Dahlia Nadkarni 
Independent RVs, Means, Variances
(continued) 
Class 9 – Mon Sept 24, 2012 
Independent RVs, Means, Variances 
Class 8 – Fri Sept 21, 2012 
Binomial Distribution (continued) birthdays.m (Matlab Example) 
Class 7 – Wed Sept 19, 2012 taught by Dahlia Nadkarni 

Class 6 – Mon Sept 17, 2012 

Class 5 – Fri Sept 14, 2012 

Class 4 – Wed Sept 12, 2012 
Example
of Probability on Infinite Discrete Sample Space 
Class 3 – Mon Sept 10, 2012 

Class 2 – Fri Sept 7, 2012 
Matlab Examples 2. Probability 3. Differential equations 3.1 Linear_System.m 3.2 The HodgkinHuxley model 
Class 1 – Wed Sept 5, 2012 
o
Organizational
matters (see Information
Sheet). o
Asking whether a
neuron fired in a given millisecond is a random experiment. o
Flipping a coin
(whether fair or biased) is also a random experiment. o
Neuron firing and
coin flipping involve two very different types of randomness. Yet both are captured
adequately in a single mathematical framework. o
General remarks
on applied math, probability and differential equations: conciseness,
generality, explanatory power, predictive power. 
Information Sheet
(includes syllabus)
MWF
2:002:50, J. Walter Wilson 301
Instructor
Elie
Bienenstock email:
firstname [at] brown [period] dam [period] edu
Office
Hours: please email me to set appointment
Computer TA
Grader