solve_ikeda_DDE2.c

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

池田遅延微分方程式と線形化した方程式

Ikeda delay differential equation (ikeda DDE) and linearized equation

solve_ikeda_DDE2.c

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

#include "ikeda_DDE2_lyap.h"

double uu[DIM+1][DIM];

void ikeda_DDE2( double x, double delay, double (*dxdt) )

{

double d1;

double d2;

d1 = sin( delay - C );

d2 = d1 * d1;

(*dxdt) = A * d2 - B * x;

}

void solve_ikeda_DDE2_using_RK4( double v[DIM], double (*dxdt), double u[DIM][DIM] )

{

int i;

int j;

double dudt;

double vv;

double delay;

double v_k1, v_k2, v_k3, v_k4;

vv = v[0];

delay = v[X_TAU];

/*******************************************************/

// vvとdelayを渡し、v_k1の計算値を得る。

// pass vv and delay, and get the calculated value of v_k1

ikeda_DDE2( vv, delay, &v_k1 );

vv = v[0] + DELTA_T * v_k1/(double)2.0;

ikeda_DDE2( vv, delay, &v_k2 );

vv = v[0] + DELTA_T * v_k2/(double)2.0;

ikeda_DDE2( vv, delay, &v_k3 );

vv = v[0] + DELTA_T * v_k3;

ikeda_DDE2( vv, delay, &v_k4 );

(*dxdt) = (v_k1 + 2.0 * v_k2 + 2.0 * v_k3 + v_k4)/(double)6.0;

vv = v[0] + DELTA_T * (*dxdt);

for ( i = 1; i < DIM; i++ ) {

v[DIM-i] = v[DIM-i-1];

}

v[0] = vv;

/*******************************************************/

// 線形化した池田遅延微分方程式を用いて微小変位ベクトルを計算

// calculate the micro-displacement vectors using linearized ikeda DDE2

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

dudt = u[DIM-1][i] * 2.0 * A * sin( delay - C ) * cos( delay - C ) - B * u[0][i];

uu[0][i] = u[0][i] + DELTA_T * dudt;

}

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

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

uu[i+1][j] = u[i][j];

u[i][j] = uu[i][j];

}

}

}