{UTF-8}
dX=
	r*X*(1-X)
	~	dmnl/time
	~		|

Initial X=
	0.01
	~	dmnl
	~		|

Previous X= DELAY FIXED (
	X,TIME STEP,X)
	~	dmnl
	~	Previous value of X for plotting
	|

r=
	r base+r ramp*(Time-INITIAL TIME)/(FINAL TIME-INITIAL TIME)
	~	1/time
	~		|

r base=
	2
	~	1/time
	~		|

r ramp=
	1
	~	1/time
	~		|

X= INTEG (
	dX,
		Initial X)
	~	dmnl
	~		|

********************************************************
	.Control
********************************************************~
		Simulation Control Paramaters
	|

FINAL TIME  = 1000
	~	time
	~	The final time for the simulation.
	|

INITIAL TIME  = 0
	~	time
	~	The initial time for the simulation.
	|

SAVEPER  = 
        TIME STEP
	~	time
	~	The frequency with which output is stored.
	|

TIME STEP  = 1
	~	time
	~	The time step for the simulation.
	|

\\\---/// Sketch information - do not modify anything except names
V300  Do not put anything below this section - it will be ignored
*View 1
$192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-0|-1--1--1|-1--1--1|96,96,100,0
10,1,X,268,69,40,20,3,3,0,0,0,0,0,0
12,2,48,80,69,10,8,0,3,0,0,-1,0,0,0
1,3,5,1,4,0,0,22,0,0,0,-1--1--1,,1|(196,69)|
1,4,5,2,100,0,0,22,0,0,0,-1--1--1,,1|(121,69)|
11,5,48,158,69,6,8,34,3,0,0,1,0,0,0
10,6,dX,158,88,12,11,32,3,0,0,-1,0,0,0
10,7,r,118,159,5,11,0,3,0,0,0,0,0,0
1,8,7,6,0,0,0,0,0,64,0,-1--1--1,,1|(133,131)|
1,9,1,6,1,0,0,0,0,64,0,-1--1--1,,1|(198,114)|
10,10,r base,80,230,21,11,0,3,0,0,0,0,0,0
1,11,10,7,0,0,0,0,0,64,0,-1--1--1,,1|(95,199)|
10,12,FINAL TIME,260,160,55,11,0,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128
1,13,12,7,0,0,0,0,0,0,0,-1--1--1,,1|(170,159)|
10,14,INITIAL TIME,270,190,60,11,0,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128
1,15,14,7,0,0,0,0,0,0,0,-1--1--1,,1|(176,170)|
10,16,r ramp,149,230,22,11,0,3,0,0,-1,0,0,0
1,17,16,7,0,0,0,0,0,0,0,-1--1--1,,1|(136,200)|
10,18,Time,240,220,26,11,0,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128
1,19,18,7,0,0,0,0,0,0,0,-1--1--1,,1|(176,188)|
12,20,0,319,294,201,11,0,4,0,0,-1,0,0,0
Logistic chaos, implemented by Tom Fiddaman, Ventana Systems
12,21,0,319,324,207,11,0,4,0,0,-1,0,0,0
For ~ continuous behavior, set 'r base' to a small number like 0.125.
12,22,0,319,354,268,11,0,4,0,0,-1,0,0,0
To generate a bifurcation diagram (see custom graphs), set 'r base' to 2 and 'r ramp' to 1
10,23,Initial X,270,20,26,11,0,3,0,0,0,0,0,0
12,24,0,319,394,260,20,8,4,0,0,-1,0,0,0
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps
10,25,Previous X,420,70,36,11,0,3,0,0,0,0,0,0
1,26,1,25,0,0,0,0,0,64,0,-1--1--1,,1|(339,69)|
1,27,23,1,0,0,0,0,0,64,1,-1--1--1,,1|(269,33)|
10,28,TIME STEP,420,100,50,11,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|0||128-128-128
1,29,28,25,0,0,0,0,0,64,0,-1--1--1,,1|(420,92)|
12,30,1508726,748,241,150,150,3,44,0,0,1,0,0,0
BIFURCATION_DIAGRAM
12,31,1574316,1106,240,150,150,3,44,0,0,1,0,0,0
X_PHASE
///---\\\
:GRAPH BIFURCATION_DIAGRAM
:TITLE Bifurcation Diagram
:X-AXIS r
:DOTS
:SCALE
:VAR X

:GRAPH X_VS_DX
:TITLE X vs dX
:X-AXIS X
:DOTS
:SCALE
:VAR dX

:GRAPH X_PHASE
:TITLE X Phase
:X-AXIS Previous X
:DOTS
:SCALE
:VAR X
:L<%^E!@
1:r2.vdf
9:r2
22:$,Dollar,Dollars,$s
22:Day,Days
22:Hour,Hours
22:Month,Months
22:Person,People,Persons
22:Unit,Units
22:Week,Weeks
22:Year,Years
23:0
15:0,0,0,0,0,0
19:100,0
27:2,
34:0,
4:Time
5:r
24:0
25:1000
26:1000