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- /*
- * phase_oscillator_ensemble.cpp
- *
- * Demonstrates the phase transition from an unsynchronized to an synchronized state.
- *
- * Copyright 2011-2012 Karsten Ahnert
- * Copyright 2011-2012 Mario Mulansky
- * Distributed under the Boost Software License, Version 1.0. (See
- * accompanying file LICENSE_1_0.txt or copy at
- * http://www.boost.org/LICENSE_1_0.txt)
- *
- */
- #include <iostream>
- #include <utility>
- #include <boost/numeric/odeint.hpp>
- #ifndef M_PI //not there on windows
- #define M_PI 3.141592653589793 //...
- #endif
- #include <boost/random.hpp>
- using namespace std;
- using namespace boost::numeric::odeint;
- //[ phase_oscillator_ensemble_system_function
- typedef vector< double > container_type;
- pair< double , double > calc_mean_field( const container_type &x )
- {
- size_t n = x.size();
- double cos_sum = 0.0 , sin_sum = 0.0;
- for( size_t i=0 ; i<n ; ++i )
- {
- cos_sum += cos( x[i] );
- sin_sum += sin( x[i] );
- }
- cos_sum /= double( n );
- sin_sum /= double( n );
- double K = sqrt( cos_sum * cos_sum + sin_sum * sin_sum );
- double Theta = atan2( sin_sum , cos_sum );
- return make_pair( K , Theta );
- }
- struct phase_ensemble
- {
- container_type m_omega;
- double m_epsilon;
- phase_ensemble( const size_t n , double g = 1.0 , double epsilon = 1.0 )
- : m_omega( n , 0.0 ) , m_epsilon( epsilon )
- {
- create_frequencies( g );
- }
- void create_frequencies( double g )
- {
- boost::mt19937 rng;
- boost::cauchy_distribution<> cauchy( 0.0 , g );
- boost::variate_generator< boost::mt19937&, boost::cauchy_distribution<> > gen( rng , cauchy );
- generate( m_omega.begin() , m_omega.end() , gen );
- }
- void set_epsilon( double epsilon ) { m_epsilon = epsilon; }
- double get_epsilon( void ) const { return m_epsilon; }
- void operator()( const container_type &x , container_type &dxdt , double /* t */ ) const
- {
- pair< double , double > mean = calc_mean_field( x );
- for( size_t i=0 ; i<x.size() ; ++i )
- dxdt[i] = m_omega[i] + m_epsilon * mean.first * sin( mean.second - x[i] );
- }
- };
- //]
- //[ phase_oscillator_ensemble_observer
- struct statistics_observer
- {
- double m_K_mean;
- size_t m_count;
- statistics_observer( void )
- : m_K_mean( 0.0 ) , m_count( 0 ) { }
- template< class State >
- void operator()( const State &x , double t )
- {
- pair< double , double > mean = calc_mean_field( x );
- m_K_mean += mean.first;
- ++m_count;
- }
- double get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / double( m_count ) : 0.0 ; }
- void reset( void ) { m_K_mean = 0.0; m_count = 0; }
- };
- //]
- int main( int argc , char **argv )
- {
- //[ phase_oscillator_ensemble_integration
- const size_t n = 16384;
- const double dt = 0.1;
- container_type x( n );
- boost::mt19937 rng;
- boost::uniform_real<> unif( 0.0 , 2.0 * M_PI );
- boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
- // gamma = 1, the phase transition occurs at epsilon = 2
- phase_ensemble ensemble( n , 1.0 );
- statistics_observer obs;
- for( double epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
- {
- ensemble.set_epsilon( epsilon );
- obs.reset();
- // start with random initial conditions
- generate( x.begin() , x.end() , gen );
- // calculate some transients steps
- integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 10.0 , dt );
- // integrate and compute the statistics
- integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 100.0 , dt , boost::ref( obs ) );
- cout << epsilon << "\t" << obs.get_K_mean() << endl;
- }
- //]
- return 0;
- }
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