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//
//
// 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<3>
{
public:
chua()
{
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);
}
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 ( std::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);
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