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
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
//
//
// chaos~
// Copyright (C) 2004 Tim Blechmann
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; see the file COPYING. If not, write to
// the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
// Boston, MA 02111-1307, USA.
#include "ode_base.hpp"
// chua system: dx1/dt = alpha * (x2 - x1 - h(x1))
// dx2/dt = x1 - x2 + x3
// dx3/dt = - beta * x2
//
// with h(x) = b*x + a - b (for x > 1)
// a*x (for -1 <= x <= 1
// b*x - a + b (for x < -1)
//
// taken from Viktor Avrutin: lecture notes
class chua:
public ode_base
{
public:
chua()
{
CHAOS_PRECONSTRUCTOR;
CHAOS_PAR_INIT(method,2);
CHAOS_PAR_INIT(dt,0.05);
CHAOS_SYS_INIT(x1,1,1);
CHAOS_SYS_INIT(x2,1,1);
CHAOS_SYS_INIT(x3,1,1);
CHAOS_PAR_INIT(a,140);
CHAOS_PAR_INIT(b,30);
CHAOS_PAR_INIT(alpha,30);
CHAOS_PAR_INIT(beta,30);
CHAOS_POSTCONSTRUCTOR;
ode_base_alloc();
}
~chua()
{
ode_base_free();
}
virtual void m_system(data_t* deriv, data_t* data)
{
data_t x1 = data[0];
data_t x2 = data[1];
data_t x3 = data[2];
data_t a = CHAOS_PARAMETER(a), b = CHAOS_PARAMETER(b);
data_t h;
if (x1 > 1)
h = b*x1 + a - b;
else if (x1 < -1)
h = b*x1 - a + b;
else
h = a*x1;
deriv[0] = CHAOS_PARAMETER(alpha) * (x2 - x1 - h);
deriv[1] = x1 - x2 + x3;
deriv[2] = - CHAOS_PARAMETER(beta) * x2;
}
virtual void m_verify()
{
data_t x1 = m_data[0];
data_t x2 = m_data[1];
data_t x3 = m_data[2];
if ( CHAOS_ABS(x3) < 1e-10)
x3 = 0;
if (x1 == 0 && x2 == 0 && x3 == 0) /* fixpoint at (0,0,0) */
{
reset();
return;
}
else
{
data_t c = m_c;
if (m_c)
{
data_t mc = - c;
if (x1 == c && x3 == mc) /* fixpoint at (c,0,-c) */
{
reset();
return;
}
if (x1 == mc && x3 == c) /* fixpoint at (-c,0,c) */
{
reset();
return;
}
}
}
}
inline void reset()
{
m_data[0] = rand_range(-1,1);
m_data[1] = rand_range(-1,1);
m_data[2] = rand_range(-1,1);
}
CHAOS_SYSVAR_FUNCS(x1, 0);
CHAOS_SYSVAR_FUNCS(x2, 1);
CHAOS_SYSVAR_FUNCS(x3, 2);
/* due to stability issues, we hook into the predicates */
data_t m_c;
bool m_pred_a(data_t a)
{
data_t b = CHAOS_PARAMETER(b);
m_c = (b - a) / (b + 1);
return true;
}
bool m_pred_b(data_t b)
{
if (b == -1)
m_c = 0;
else
{
data_t a = CHAOS_PARAMETER(a);
m_c = (b - a) / (b + 1);
}
return true;
}
CHAOS_SYSPAR_FUNCS_PRED(a, m_pred_a);
CHAOS_SYSPAR_FUNCS_PRED(b, m_pred_b);
CHAOS_SYSPAR_FUNCS(alpha);
CHAOS_SYSPAR_FUNCS(beta);
};
#define CHUA_CALLBACKS \
ODE_CALLBACKS; \
CHAOS_SYS_CALLBACKS(alpha); \
CHAOS_SYS_CALLBACKS(beta); \
CHAOS_SYS_CALLBACKS(a); \
CHAOS_SYS_CALLBACKS(b); \
CHAOS_SYS_CALLBACKS(x1); \
CHAOS_SYS_CALLBACKS(x2); \
CHAOS_SYS_CALLBACKS(x3);
#define CHUA_ATTRIBUTES \
ODE_ATTRIBUTES; \
CHAOS_SYS_ATTRIBUTE(a); \
CHAOS_SYS_ATTRIBUTE(b); \
CHAOS_SYS_ATTRIBUTE(alpha); \
CHAOS_SYS_ATTRIBUTE(beta); \
CHAOS_SYS_ATTRIBUTE(x1); \
CHAOS_SYS_ATTRIBUTE(x2); \
CHAOS_SYS_ATTRIBUTE(x3);
|
