public float calc_Fox_Runge_Kutta(float f, float r, float ts)
{
Rabbit rab = new Rabbit();
Fox fx = new Fox();
float k1 = 0;
float k2 = 0;
float k3 = 0;
float k4 = 0;
float n1 = 0;
float n2 = 0;
float n3 = 0;
k1 = fx.fox_model(f, r); //f(y)
n1 = rab.rabbit_model(r, f);
float tmp = f + (ts / 2) * k1;
float tmp2 = r + (ts / 2) * n1;
k2 = fx.fox_model((tmp), tmp2); //f(y+(h/2)k1)
n2 = rab.rabbit_model(tmp2, tmp);
tmp = f + (ts / 2) * k2;
tmp2 = r + (ts / 2) * n2;
k3 = fx.fox_model((tmp), tmp2); //f(y+(h/2)k2)
n3 = rab.rabbit_model(tmp2, tmp);
tmp = f + ts * k3;
tmp2 = r + (ts / 2) * n3;
k4 = fx.fox_model((tmp), tmp2); //f(y+ hk3)
f = f + ts * (k1 + 2 * k2 + 2 * k3 + k4) / 6; //y + h*(k1 + 2 * k2 + 2 * k3 + k4)/6
return f;
}
public float calc_Rabbit_Runge_Kutta(float r, float f, float ts)
{
Rabbit rab = new Rabbit();
Fox fx = new Fox();
float k1 = 0;
float k2 = 0;
float k3 = 0;
float k4 = 0;
float m1 = 0;
float m2 = 0;
float m3 = 0;
//k1 = rproxy.pop_inc(r, f); //f(y)
k1 = rab.rabbit_model(r, f);
m1 = fx.fox_model(f, r);
float tmp = r + (ts / 2) * k1;
float tmp2 = f + (ts / 2) * m1;
//k2 = rproxy.pop_inc((tmp), f); //f(y+(h/2)k1)
k2 = rab.rabbit_model((tmp), tmp2);
m2 = fx.fox_model((tmp2), tmp);
tmp = r + (ts / 2) * k2;
tmp2 = f + (ts / 2) * m2;
//k3 = rproxy.pop_inc((tmp), f); //f(y+(h/2)k2)
k3 = rab.rabbit_model((tmp), tmp2);
m3 = fx.fox_model((tmp2), tmp);
tmp = r + ts * k3;
tmp2 = f + ts * m3;
//k4 = rproxy.pop_inc((tmp), f); //f(y+ hk3)
k4 = rab.rabbit_model((tmp), tmp2);
//y + h*(k1 + 2 * k2 + 2 * k3 + k4)/6
r = r + ts * (k1 + 2 * k2 + 2 * k3 + k4) / 6;
return r;
}
public double[,] rabbit_fox_horizontal_diff_ts(float r, float r_ts, float f, float f_ts, int yr, string r_integ_method, string f_integ_method)
{
int ts_factor = 10; //time step factor, to define numer of loops in unit of time, e.g. if ts=0.1 then we will have 10 loops in each unit of time
float ts;
if (r_ts > f_ts)
ts = f_ts;
else if (r_ts > f_ts)
ts = r_ts;
else
ts = r_ts;
if (ts >= 0.1)
{
ts_factor = 10;
}
else if (ts >= 0.009) //>=0.01
{
ts_factor = 100;
}
else if (ts >= 0.0009) //>=0.001
ts_factor = 1000;
//ts_factor = 1000;
Rabbit rab = new Rabbit();
Fox fx_m = new Fox();
RungeKutta rk = new RungeKutta();
//the system will loop for each time step
//int lp = Convert.ToInt32(Math.Truncate(yr / 0.1)); //total number of loop due to the defined year
int lp = yr * ts_factor;
lp = lp + 1;
// r_result = new double[lp]; //array for rab
//f_result = new double[lp]; //array for fox
double[,] result = new double[lp, 2];
double[] t = new double[3];
t[1] = Convert.ToDouble(r_ts.ToString("#.####")); //time step of rabbit
t[2] = Convert.ToDouble(f_ts.ToString("#.####")); //time step of fox
int temp_r_ts = Convert.ToInt16(r_ts * ts_factor);
int temp_f_ts = Convert.ToInt16(f_ts * ts_factor);
float rx = r;
float ry = f;
float fx = r;
float fy = f;
for (int i = 1; i < lp; i++)
{
int m = i % temp_r_ts; //m for maintaining result of % operation
if (m == 0 && i > 0) //check if the current time step is valid to run rabit model
{
if (r_integ_method == "Runge-Kutta") // Runge-Kutta integration of rabbit model
{
rx = rk.calc_Rabbit_Runge_Kutta(rx, ry, r_ts);
}
else
rx = rx + rab.rabbit_model(rx, ry) * r_ts;
//rx = rx + rabbit_with_diff_func(rx, ry) * r_ts;
r = rx;
}
int n = i % temp_f_ts;
if (n == 0 && i > 0) //check if the current time step is valid to run fox model
{
if (m == 0)
fx = r;
if (f_integ_method == "Runge-Kutta") // for Runge-Kutta integration of fox model
{
fy = rk.calc_Fox_Runge_Kutta(fy, fx, f_ts);
}
else
fy = fy + fx_m.fox_model(fy, fx) * f_ts;
//fy = fy + fox_with_diff_func(fy, fx) * f_ts;
f = fy;
fx = r;
}
if (m == 0) //if the time step meets ts of rabbit then copy value of f
ry = f;
//r_result[i] = r; // Convert.ToDouble(r.ToString("#.##"));
result[i,0] = r;
if (f >= 0)
//f_result[i] = f;
result[i, 1] = f;
else //if fox pop <0 set it to 0
{
f = 0;
//f_result[i] = 0;
result[i, 1] = 0;
}
if (result[i, 0] < 0) // (r_result[i] < 0)
{
//r_result[i] = 0;//if rab pop<0 then set the pop value to 0 and quit
//f_result[i] = 0;
result[i, 0] = 0;//if rab pop<0 then set the pop value to 0 and quit
result[i, 1] = 0;
break;
}
}
return result;
}
public double[,] rabbit_fox_horizontal_same_ts(float r, float f, int yr, float ts, string r_integ_method, string f_integ_method)
{
int ts_factor = 10; //time step factor, to define numer of loops in unit of time, e.g. if ts=0.1 then we will have 10 loops in each unit of time
if (ts >= 0.1)
{
ts_factor = 10;
}
else if (ts >= 0.009) //>=0.01
{
ts_factor = 100;
}
else if (ts >= 0.0009) //>=0.001
ts_factor = 1000;
//ts_factor = 1000;
Rabbit rab = new Rabbit();
Fox fx = new Fox();
RungeKutta rk = new RungeKutta();
//the system will loop according to the defined time step
//int lp = Convert.ToInt16(Math.Truncate(yr / ts)); //total number of loop due to the defined time step
//int lp = Convert.ToInt32(Math.Truncate(yr / 0.1)); //10 timestep in 1 year
int lp = yr * ts_factor;
lp = lp + 2;
double[,] result = new double[lp, 2];
float fr = r; //rabbit population for fox model
for (int i = 1; i < lp; i++)
{
//if (i % (Convert.ToInt16(Math.Truncate(ts * 10))) == 0)
if (i % (Convert.ToInt16(ts * ts_factor)) == 0)
{
//run rabbit model
if (r_integ_method == "Runge-Kutta") // for Runge-Kutta integration of rabbit
{
r = rk.calc_Rabbit_Runge_Kutta(r, f, ts);
}
else
//for euler integration
r = r + rab.rabbit_model(r, f) * ts;
// r = r + rabbit_with_diff_func(r, f) * ts; //rabbit with px/(q+x) function than bx
//run fox model
if (f_integ_method == "Runge-Kutta") // for Runge-Kutta integration of fox model
{
f = rk.calc_Fox_Runge_Kutta(f, fr, ts);
}
else
f = f + fx.fox_model(f, fr) * ts;
//f = f + fox_with_diff_func(f, fr) * ts; //fox with px/(q+x) function than bx
fr = r; //update current rabbit population for fox model
if (r < 0)
result[i, 0] = 0;
else
result[i, 0] = r; //Convert.ToDouble(r.ToString("#.##"));
if (f < 0)
result[i, 1] = 0;
else
result[i, 1] = f; // Convert.ToDouble(f.ToString("#.##"));
if (result[i, 0] < 0) //(result[i, 0] < 1)
{
result[i, 0] = 0; //if pop<0 then set the pop value to 0
result[i, 1] = 0;
break;
}
}
else
{
if (r < 0) //(result[i, 0] < 1)
{
result[i, 0] = 0; //if pop<0 then set the pop value to 0
result[i, 1] = 0;
break;
}
else
{
result[i, 0] = r;
result[i, 1] = f;
}
}
}
return result;
}