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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 van_der_pol:
// d2u/dt2 + a*(u*u -1)*du/dt + u = k * cos(Omega*t)
// equivalent:
// du1/dt = u2
// du2/dt = -a*(u1*u1 - 1)*u2 - u1 + k*cos(u3)
// du3/dt = Omega
// taken from Willi-Hans Steeb: Chaos and Fractals
class driven_van_der_pol
: public ode_base<3>
{
public:
driven_van_der_pol()
{
CHAOS_PAR_INIT(method,2);
CHAOS_PAR_INIT(dt,0.01);
CHAOS_SYS_INIT(u1,0.8, 0);
CHAOS_SYS_INIT(u2,0.6, 1);
CHAOS_SYS_INIT(u3,0.4, 2);
CHAOS_PAR_INIT(a,5);
CHAOS_PAR_INIT(Omega,2.466);
CHAOS_PAR_INIT(k,5);
}
virtual void m_system(data_t* deriv, data_t* data)
{
data_t u1 = data[0], u2 = data[1], u3 = data[2];
deriv[0] = u2;
deriv[1] = - CHAOS_PARAMETER(a) * (u1*u1 -1) * u2 - u1 +
CHAOS_PARAMETER(k)*cos(u3);
deriv[2] = CHAOS_PARAMETER(Omega);
}
virtual void m_verify()
{
/* make sure to stay in the range of 2 pi */
if (m_data[2] > 2*M_PI)
m_data[2] = chaos_mod(m_data[2], 2*M_PI);
}
CHAOS_SYSVAR_FUNCS(u1, 0);
CHAOS_SYSVAR_FUNCS(u2, 1);
CHAOS_SYSVAR_FUNCS(u3, 2);
CHAOS_SYSPAR_FUNCS(a);
CHAOS_SYSPAR_FUNCS(k);
CHAOS_SYSPAR_FUNCS(Omega);
};
#define DRIVEN_VAN_DER_POL_CALLBACKS \
ODE_CALLBACKS; \
CHAOS_SYS_CALLBACKS(u1); \
CHAOS_SYS_CALLBACKS(u2); \
CHAOS_SYS_CALLBACKS(u3); \
CHAOS_SYS_CALLBACKS(a); \
CHAOS_SYS_CALLBACKS(k); \
CHAOS_SYS_CALLBACKS(Omega);
#define DRIVEN_VAN_DER_POL_ATTRIBUTES \
ODE_ATTRIBUTES; \
CHAOS_SYS_ATTRIBUTE(u1); \
CHAOS_SYS_ATTRIBUTE(u2); \
CHAOS_SYS_ATTRIBUTE(u3); \
CHAOS_SYS_ATTRIBUTE(a); \
CHAOS_SYS_ATTRIBUTE(k); \
CHAOS_SYS_ATTRIBUTE(Omega);
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