roessler_lyap.h

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

レスラー方程式のリアプノフスペクトラムの計算

calculating the Lyapunov spectrum of the Roessler equations

dx/dt = -y - z

dy/dt = x + A * y

dz/dt = B + z * (x - C)

roessler_lyap.h

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

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define ITERATION 10000000

#define SKIP 100000

#define DELTA_T 0.01 /* step size of the fourth-order Runge-Kutta method */

// 初期値

// initial values

#define X0 1.0

#define Y0 1.1

#define Z0 1.2

// parameters

#define A 0.2

#define B 0.2

#define C 5.7

/* Lyapunov spectrum (log with base-e)

0.0718, 0, -5.3944 when DELTA_T is 0.01

0.0675, 0, -4.9815 when DELTA_T is 0.12

*/

// 変数の数

// number of variables

#define DIM 3

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

extern void solve_roessler_eqs_using_RK4( double v[DIM], double u[DIM][DIM] );

extern void roessler_eqs( double v[DIM], double dfu[DIM][DIM], double dvdt[DIM], double df_k[DIM][DIM] );

extern void gram_schmidt_orth( double u[DIM][DIM], double e[DIM][DIM] );

extern double calc_lyap_dim( double lambda[DIM] );

extern double log2( double x );