A Computational Approach To Understanding the Neuronal Control of Leech Swimming

LEECH SWIM INITIATION PATHWAY

Cell TR1 SWIM VARIABILITY

SOURCE OF VARIABILITY


PURPOSE

EXPERIMENT

 

 

NONLINEAR TIME SERIES ANALYSIS

Background

Lorenz

dx/dt = a (y – z)

dy/dt = x (R – z) – y

dz/dt = xy – bz

where a = 16, R=45.92, and b=4.

Time series plot

State space

Embedding

 

Suppose we have a time series,

x(t) = {x1, x2, …, xN}

let m = 3, and L = 5,

We get vectors of the form;

X1 = (x1, x6, x11)

X2 = (x2, x7, x12)

X3 = (x3, x8, x13)

ß

Xn = (xN-11, xN-5, xN)

 

Reconstructed state space