# Two Dimensional Maps - Equations

## Henon Map

 xn+1 = yn + 1 - a xn2 yn+1 = b xn2

## Circle Map

 xn+1 = xn + c + yn+1/2 yn+1 = b yn - a sin(2xn)

## Duffing Map

 xn+1 = yn yn+1 = - b xn + a yn - yn3

## Baker's Map

 xn+1 = b xn yn+1 = yn/a if yn < a xn+1 = (1 - c) + c xn yn+1 = (yn - a)/(1 - a) if yn > a

## Kaplan-Yorke Map

 xn+1 = a xn mod 1 yn+1 = - b yn + cos(2xn)

## Standard Map

 xn+1 = xn + yn+1/2 yn+1 = yn + a sin(2xn)

## Grebogi-Ott-Yorke Map

 xn+1 = xn + w1 +a P1(xn,yn) mod 1 yn+1 = yn + w2 +a P2(xn,yn) mod 1

The nonlinear functions Pi are sums of sinusoidal functions A (i)rs sin[2(rx+sy+B (i)rs )], with (r,s)=(0,1),(1,0),(1,1), or (1,-1). GOY selected a set of A (i)rs,B (i)rs randomly in the range 0 to 1:

 r,s A (1)rs B (1)rs A (2)rs B (2)rs 1,0 -0.26813663648754 0.98546084298505 0.08818611671542 0.99030722865609 0,1 -0.91067559396390 0.50446045609351 -0.56502889980448 0.33630697012268 1,1 0.31172026382793 0.94707472523078 0.16299548727086 0.29804921230971 1,-1 -0.04003977835470 0.23350105508507 -0.80398881978155 0.15506467277737

The parameter k=0.107, and then a gives the strength of the nonlinearity with a=1 corresponding to the point at which the map (for these values of A,B) becomes noninvertible.

The parameters w1 and w2 are reset with random values between 0 and 1 each time the evolution is reset using the "Reset" button or by clicking outside the stopped plot.

## Sinai Map

 xn+1 = xn + yn + a cos(2yn) mod 1 yn+1 = xn + 2 yn mod 1

[Instructions]