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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);
+ }
+
+
+
+ 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);
+ }
+
+ void m_verify()
+ {
+ /* make sure to stay in the range of 2 pi */
+ if (m_data[2] > 2*M_PI)
+ m_data[2] = std::fmod(m_data[2], data_t(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);