Lotka-Volterra C++

#include<iostream>
#include<fstream>
#include<sstream>
#include<iomanip>
using namespace std;

const double a = 0.05;
const double b = 0.002;
const double c = 0.06;
const double d = 0.004;

const double step = 0.1;

const int numberOfLoops = 4000;


double dxdt(double x, double y){
    return x*(a - b*y);
}

double dydt(double x, double y){
    return -y*(c - d*x);
}

int main(int argc, char** argv){

    // x -> prey
    // y -> predator

    double y0Step = 1;

    for(int i1 = 0; i1 < 100; i1++){

        double x0 = 100;
        double y0 = 10+i1*y0Step;

        double x = x0;
        double y = y0;


        ofstream af;
        stringstream afN; afN << "./txt/xt" << setfill('0') << setw(4) << i1 << ".txt";
        string afName = afN.str();

        ofstream bf;
        stringstream bfN; bfN << "./txt/yt" << setfill('0') << setw(4) << i1 << ".txt";
        string bfName = bfN.str();

        af.open(afName);
        bf.open(bfName);

        for(double i1 = 0; i1 < numberOfLoops * step ; i1 += step){

            af << i1 << ' ' << x << endl;
            bf << i1 << ' ' << y << endl;

            x0=x;
            y0=y;

            x += step * dxdt(x0,y0);
            y += step * dydt(x0,y0);
        }

        af.close();
        bf.close();

        stringstream commandsToTerminal;
        commandsToTerminal << "gnuplot -p -e \"set term png; set output \'"
                            << "./png/doublePlot" << setfill('0') << setw(4) << i1 << ".png"
                            << "\';plot \'" << afN.str() << "\', \'" << bfN.str() << "\'\" ";

        system(commandsToTerminal.str().c_str());
    }


    system("convert -delay 10 -loop 0 ./png/*.png animation.gif && open -a /Applications/Google\\ Chrome.app/ animation.gif");

    // Any argument clears the unnecessary aux files
    if(argc > 1){
        system("rm ./png/* ./txt/*");
    }

    return 0;
}