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120 lines
3.0 KiB
C++
120 lines
3.0 KiB
C++
/*
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* chaotic_system.cpp
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*
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* This example demonstrates how one can use odeint to determine the Lyapunov
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* exponents of a chaotic system namely the well known Lorenz system. Furthermore,
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* it shows how odeint interacts with boost.range.
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*
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* Copyright 2011-2012 Karsten Ahnert
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* Copyright 2011-2013 Mario Mulansky
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*
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* Distributed under the Boost Software License, Version 1.0.
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* (See accompanying file LICENSE_1_0.txt or
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* copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#include <iostream>
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#include <boost/array.hpp>
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#include <boost/numeric/odeint.hpp>
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#include "gram_schmidt.hpp"
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using namespace std;
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using namespace boost::numeric::odeint;
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const double sigma = 10.0;
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const double R = 28.0;
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const double b = 8.0 / 3.0;
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//[ system_function_without_perturbations
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struct lorenz
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{
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template< class State , class Deriv >
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void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
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{
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typename boost::range_iterator< const State >::type x = boost::begin( x_ );
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typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
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dxdt[0] = sigma * ( x[1] - x[0] );
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dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
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dxdt[2] = -b * x[2] + x[0] * x[1];
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}
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};
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//]
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//[ system_function_with_perturbations
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const size_t n = 3;
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const size_t num_of_lyap = 3;
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const size_t N = n + n*num_of_lyap;
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typedef boost::array< double , N > state_type;
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typedef boost::array< double , num_of_lyap > lyap_type;
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void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
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{
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lorenz()( x , dxdt , t );
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for( size_t l=0 ; l<num_of_lyap ; ++l )
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{
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const double *pert = x.begin() + 3 + l * 3;
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double *dpert = dxdt.begin() + 3 + l * 3;
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dpert[0] = - sigma * pert[0] + 10.0 * pert[1];
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dpert[1] = ( R - x[2] ) * pert[0] - pert[1] - x[0] * pert[2];
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dpert[2] = x[1] * pert[0] + x[0] * pert[1] - b * pert[2];
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}
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}
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//]
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int main( int argc , char **argv )
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{
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state_type x;
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lyap_type lyap;
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fill( x.begin() , x.end() , 0.0 );
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x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
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const double dt = 0.01;
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//[ integrate_transients_with_range
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// explicitly choose range_algebra to override default choice of array_algebra
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runge_kutta4< state_type , double , state_type , double , range_algebra > rk4;
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// perform 10000 transient steps
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integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
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//]
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//[ lyapunov_full_code
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fill( x.begin()+n , x.end() , 0.0 );
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for( size_t i=0 ; i<num_of_lyap ; ++i ) x[n+n*i+i] = 1.0;
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fill( lyap.begin() , lyap.end() , 0.0 );
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double t = 0.0;
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size_t count = 0;
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while( true )
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{
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t = integrate_n_steps( rk4 , lorenz_with_lyap , x , t , dt , 100 );
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gram_schmidt< num_of_lyap >( x , lyap , n );
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++count;
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if( !(count % 100000) )
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{
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cout << t;
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for( size_t i=0 ; i<num_of_lyap ; ++i ) cout << "\t" << lyap[i] / t ;
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cout << endl;
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}
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}
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//]
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return 0;
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}
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