/*-----------------------------------------------------------------
ティンカーベル写像のリアプノフスペクトラムの計算
calculating the Lyapunov spectrum of the Tinkerbell map
x[t+1] = x[t] * x[t] - y[t] * y[t] + A * x[t] + B * y[t]
y[t+1] = 2.0 * x[t] * y[t] + C * x[t] + D * y[t]
tinkerbell_lyap.c
-----------------------------------------------------------------*/
#include "tinkerbell_lyap.h"
int main(void)
{
int i;
int j;
int t;
double x;
double y;
double d2;
double lyap_dim;
double lyap[DIM]; /* リアプノフ指数, Lyapunov exponent */
double u[DIM][DIM];
double e[DIM][DIM];
/*------------------------------------------------------------------*/
// 直交化した長さ１のベクトル（単位行列）uの作成
// create orthogonalized vectors u with length 1 (unit matrix)
for ( i = 0; i < DIM; i++ ) {
for ( j = 0; j < DIM; j++ ) {
u[i][j] = ( i == j ? 1.0 : 0.0 );
// printf("%lf ", u[i][j]);
}
// printf("\n");
lyap[i] = 0.0;
}
/*------------------------------------------------------------------*/
// 初期値の設定
// set the initial values
x = X0;
y = Y0;
/*------------------------------------------------------------------*/
for( t = 0; t < SKIP; t++ ){
// ティンカーベル写像の値とヤコビ行列の計算
// calculate the Tinkerbell map and the Jacobian matrix
tinkerbell_eqs( &x, &y, u );
// printf("%.10lf %.10lf\n", x, y); /* output the data */
}
/*------------------------------------------------------------------*/
// uの再設定
// reset vector u
for ( i = 0; i < DIM; i++ ) {
for ( j = 0; j < DIM; j++ ) {
u[i][j] = ( i == j ? 1.0 : 0.0 );
}
}
/*------------------------------------------------------------------*/
for( t = 0; t < ITERATION; t++ ){
// ティンカーベル写像の値とヤコビ行列の計算
// calculate the Tinkerbell map and the Jacobian matrix
tinkerbell_eqs( &x, &y, u );
// printf("%.10lf %.10lf\n", x, y); /* output the data */
// グラム・シュミットの正規直交化法
// Gram-Schmidt orthogonalisation
gram_schmidt_orth( u, e );
// リアプノフ指数の計算
// calculate the Lyapunov exponents
for ( j = 0; j < DIM; j++ ) {
d2 = 0.0;
for ( i = 0; i < DIM; i++ ) {
d2 += e[i][j] * e[i][j];
}
lyap[j] += log( sqrt( d2 ) );
// lyap[j] += log2( sqrt( d2 ) );
// printf( "%.10lf ", lyap[j]/(double)(t+1) );
}
// printf("\n");
}
/*------------------------------------------------------------------*/
for ( i = 0; i < DIM; i++ ) {
lyap[i] = lyap[i]/(double)ITERATION;
}
// リアプノフ次元の計算
// calculate the Lyapunov dimension
lyap_dim = calc_lyap_dim( lyap );
printf("#----------------------------------------------\n" );
printf("# ITERATION: %d\n", (int)ITERATION);
printf("# SKIP: %d\n", (int)SKIP);
printf("#----------------------------------------------\n" );
printf("# initial condition\n");
printf("# x0: %g\n", X0);
printf("# y0: %g\n", Y0);
printf("#----------------------------------------------\n" );
printf("# A = %g, B = %g, C = %g, D = %g\n", (double)A, (double)B, (double)C, (double)D );
printf("#----------------------------------------------\n" );
printf("# Lyapunov Spectrum (log with base-e)\n" );
printf("# lyap[1]: %lf\n", lyap[0] );
printf("# lyap[2]: %lf\n", lyap[1] );
printf("# Lyapunov Dimension: %lf\n", lyap_dim );
printf("#----------------------------------------------\n" );
d2 = lyap[0] + lyap[1];
printf("# lyap[1]+lyap[2]: %lf\n", d2 );
return 0;
}
/*----------------------------------------------------------------------------*/
double log2( double x )
{
return log(x)/(double)log(2.0);
}
/*----------------------------------------------------------------------------*/
// リアプノフ次元の計算
// calculate Lyapunov dimension
double calc_lyap_dim( double lyap[DIM] )
{
int i;
double sum;
double lyap_dim = (double)DIM;
sum = 0.0;
for ( i = 0; i < (int)DIM; i++ ) {
sum += lyap[i];
if ( sum < 0.0 ) {
lyap_dim = i + (sum - lyap[i])/(double)fabs( lyap[i] );
break;
}
}
return lyap_dim;
}