1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998)
originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>Basic Functionality</TITLE>
<META NAME="description" CONTENT="Basic Functionality">
<META NAME="keywords" CONTENT="userman">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
<LINK REL="STYLESHEET" HREF="userman.css">
<LINK REL="next" HREF="node36.html">
<LINK REL="previous" HREF="node34.html">
<LINK REL="up" HREF="node34.html">
<LINK REL="next" HREF="node36.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html981"
HREF="node36.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="/usr/lib/latex2html/icons.gif/next_motif.gif"></A>
<A NAME="tex2html978"
HREF="node34.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="/usr/lib/latex2html/icons.gif/up_motif.gif"></A>
<A NAME="tex2html972"
HREF="node34.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="/usr/lib/latex2html/icons.gif/previous_motif.gif"></A>
<A NAME="tex2html980"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="/usr/lib/latex2html/icons.gif/contents_motif.gif"></A>
<BR>
<B> Next:</B> <A NAME="tex2html982"
HREF="node36.html">Periodic Variables</A>
<B> Up:</B> <A NAME="tex2html979"
HREF="node34.html">Defining Dynamical Systems Using</A>
<B> Previous:</B> <A NAME="tex2html973"
HREF="node34.html">Defining Dynamical Systems Using</A>
<BR>
<BR>
<!--End of Navigation Panel-->
<H2><A NAME="SECTION00511000000000000000"> </A><A NAME="1694"> </A>
<BR>
Basic Functionality
</H2>
<P>
The basic defining equations for a dynamical system are
entered in the following format:
<P>
<PRE>
# The Lorenz system (lorenz.def)
x' = sigma ( y - x )
y' = rho x - y - x z
z' = -beta z + x y
INITIAL sigma 10 rho 28 beta 2.6667
</PRE>
<P>
We denote the time derivative of a variable by a prime, <TT>'</TT>. This is followed by
an equals sign and then the right hand side. A mapping is input in the
same format using the prime to indicate the new point in phase space.
Variable and parameter names are alphanumeric strings beginning with an
alphabetic character.
Any undefined string is understood to be a parameter in the system.
<P>
Comments are allowed at the end of any line and must
begin with the pound character, #.
As seen in the above example, multiplication is understood,
when no arithmetic operator is present, but it may be
explicitly indicated with an asterisk, *.
The INITIAL declaration assigns initial values to the parameters.
<P>
The parser understands the following fundamental constants, operators, and
special functions:
<P>
<PRE>
constants: PI, pi, E
operators: +, -, *, /, % (mod), ^
special functions: sin, cos, tan, asin, acos, atan, sinh, cosh,
tanh, log, ln, exp, abs, sqrt
</PRE>The special functions all correspond to standard C math library functions.
<P>
If you try this example, set the dynamical system type setting to Vector field, and
then select the ``Build model'' button on the Parser window in order to
create the dynamical system from the text.
<P>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html981"
HREF="node36.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="/usr/lib/latex2html/icons.gif/next_motif.gif"></A>
<A NAME="tex2html978"
HREF="node34.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="/usr/lib/latex2html/icons.gif/up_motif.gif"></A>
<A NAME="tex2html972"
HREF="node34.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="/usr/lib/latex2html/icons.gif/previous_motif.gif"></A>
<A NAME="tex2html980"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="/usr/lib/latex2html/icons.gif/contents_motif.gif"></A>
<BR>
<B> Next:</B> <A NAME="tex2html982"
HREF="node36.html">Periodic Variables</A>
<B> Up:</B> <A NAME="tex2html979"
HREF="node34.html">Defining Dynamical Systems Using</A>
<B> Previous:</B> <A NAME="tex2html973"
HREF="node34.html">Defining Dynamical Systems Using</A>
<!--End of Navigation Panel-->
<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
</ADDRESS>
</BODY>
</HTML>
|
