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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"
#include <cmath>
// driven anharmonic:
// d2u/dt2 + a * du/dt + b*u + c * u*u*u = k1 + k2*cos(Omega*t)
// equivalent:
// du1/dt = u2
// du2/dt = -a*u2 - b*u1 -c*u*u*u + k1 + k2*cos(Omega*t)
// taken from Willi-Hans Steeb: Chaos and Fractals
class driven_anharmonic
: public ode_base<2>
{
public:
driven_anharmonic()
{
CHAOS_PAR_INIT(method,0);
CHAOS_PAR_INIT(dt,0.01);
CHAOS_SYS_INIT(u1,0,0);
CHAOS_SYS_INIT(u2,1,1);
CHAOS_PAR_INIT(a,1);
CHAOS_PAR_INIT(b,-10);
CHAOS_PAR_INIT(c,100);
CHAOS_PAR_INIT(Omega,3.5);
CHAOS_PAR_INIT(k1,0.01);
CHAOS_PAR_INIT(k2,1);
m_t = 0;
}
virtual void m_system(data_t* deriv, data_t* data)
{
data_t u1 = data[0], u2 = data[1];
deriv[0] = u2;
deriv[1] = - CHAOS_PARAMETER(a) * u2 - CHAOS_PARAMETER(b) * u1 -
CHAOS_PARAMETER(c) * u1*u1*u1 + CHAOS_PARAMETER(k1) +
CHAOS_PARAMETER(k2) * cos (CHAOS_PARAMETER(Omega) * m_t);
m_t += m_dt;
if (m_t > 2 * M_PI)
m_t = fmod(m_t, (data_t)(M_PI*2));
}
data_t m_t;
CHAOS_SYSVAR_FUNCS(u1, 0);
CHAOS_SYSVAR_FUNCS(u2, 1);
CHAOS_SYSPAR_FUNCS(a);
CHAOS_SYSPAR_FUNCS(b);
CHAOS_SYSPAR_FUNCS(c);
CHAOS_SYSPAR_FUNCS(k1);
CHAOS_SYSPAR_FUNCS(k2);
CHAOS_SYSPAR_FUNCS(Omega);
};
#define DRIVEN_ANHARMONIC_CALLBACKS \
ODE_CALLBACKS; \
CHAOS_SYS_CALLBACKS(u1); \
CHAOS_SYS_CALLBACKS(u2); \
CHAOS_SYS_CALLBACKS(a); \
CHAOS_SYS_CALLBACKS(b); \
CHAOS_SYS_CALLBACKS(c); \
CHAOS_SYS_CALLBACKS(k1); \
CHAOS_SYS_CALLBACKS(k2); \
CHAOS_SYS_CALLBACKS(Omega);
#define DRIVEN_ANHARMONIC_ATTRIBUTES \
ODE_ATTRIBUTES; \
CHAOS_SYS_ATTRIBUTE(u1); \
CHAOS_SYS_ATTRIBUTE(u2); \
CHAOS_SYS_ATTRIBUTE(a); \
CHAOS_SYS_ATTRIBUTE(b); \
CHAOS_SYS_ATTRIBUTE(c); \
CHAOS_SYS_ATTRIBUTE(k1); \
CHAOS_SYS_ATTRIBUTE(k2); \
CHAOS_SYS_ATTRIBUTE(Omega);
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