solve_hyperchaos_map_eqs.c

/*------------------------------------------------------------------------

ハイパーカオス写像とヤコビ行列（線形化したハイパーカオス写像）

Hyperchaos map and the Jacobian (linearized Hyperchaos map)

solve_hyperchaos_map_eqs.c

------------------------------------------------------------------------*/

#include "hyperchaos_map_lyap.h"

void hyperchaos_map_eqs( double (*x), double (*y), double (*z), double u[DIM][DIM] )

{

int i, j, k;

double xx;

double yy;

double zz;

double d2;

double df[DIM][DIM];

double dfu[DIM][DIM];

// ハイパーカオス写像

// Hyperchaos map

xx = 3.8 * (*x) * ( 1.0 - (*x) ) - 0.05 * ( (*y) + 0.35 ) * ( 1.0 - 2.0 * (*z) );

yy = 0.1 * (( (*y) + 0.35 ) * ( 1.0 - 2.0 * (*z) ) - 1.0 ) * ( 1.0 - 1.9 * (*x) );

zz = 3.78 * (*z) * ( 1.0 - (*z) ) + 0.2 * (*y);

(*x) = xx;

(*y) = yy;

(*z) = zz;

// ヤコビ行列

// Jacobian  matrix

df[0][0] = 3.8 - 7.6 * (*x); 

df[0][1] = -0.05 + 0.1 * (*z);

df[0][2] = 0.1 * (*y) + 0.035;

df[1][0] = -0.19 * (*y) + 0.38 * (*y) * (*z) + 0.133 * (*z) + 0.1235;

df[1][1] = 0.1 - 0.2 * (*z) - 0.19 * (*x) + 0.38 * (*x) * (*z);

df[1][2] = -0.2 * (*y) - 0.07 + 0.38 * (*x) * (*y) + 0.133 * (*x);

df[2][0] = 0.0;

df[2][1] = 0.2;

df[2][2] = 3.78 - 7.56 * (*z);

/*

｜ df[0][0]  df[0][1]  df[0][2] ｜

｜ ｜

df = ｜ df[1][0]  df[1][1]  df[1][2] ｜

｜ ｜

｜ df[2][0]  df[2][1]  df[2][2] ｜

*/

// ヤコビ行列を用いて微小変位ベクトルを計算

// calculate the micro-displacement vector using the Jacobian matrix

for ( i = 0; i < DIM; i++ ) {

for ( j = 0; j < DIM; j++ ) {

d2 = 0.0;

for ( k = 0; k < DIM; k++ ) {

d2 += df[i][k] * u[k][j];

}

dfu[i][j] = d2;

}

}

for ( i = 0; i < DIM; i++ ) {

for ( j = 0; j < DIM; j++ ) {

u[i][j] = dfu[i][j];

}

}

}