[C language] Issue in the Lotka-Volterra model.

[ander]

Hello guys, im a beginner programer and I need help with my simulation of the Lotka-Volterra model. I have to implement Euler and Verlet algorithm and I dont know if it is well done. In the model there is constant, V, my problem is that V is not conserved in time and I dont know why. I don't know what problems my code has, nor do I know if the results it gives me so far are correct. I need help, I leave the code here, thank you very much.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define dt 0.0625
#define MAX 400
#define EULER

void feuler(double xn,double yn,double *xnext,double *ynext);
void fverlet(double xn,double yn,double *xnext,double *ynext);

double Cxx=1.0;
double Cxy=0.2;
double Cyy=0.2;
double Cyx=0.01;

int main()
    {
    double x;
    double y;
    double t;
    double xaux,yaux;
    double V,Vaux;
    FILE *f;

    x=20;
    y=6;
    t=0;
    f=fopen("PyD.txt","w");

    if (f==NULL)
    {
        printf("ERROR");
    }

    else{

    Vaux=Cyx*x-Cyy*log(x)+Cxy*y-Cxx*log(y);
    fprintf(f,"    t\t\t    x\t\t    y\t\t    V\t\t   dx_dt\t   dy_dt\n%lf\t%lf\t%lf\t%lf\t%lf\t %lf\n",t,x,y,Vaux,Cxx*x-Cxy*x*y,Cyx*x*y-Cyy*y);


    #ifdef EULER

        for(t=0;t<=MAX;t+=dt) // Este bucle representa el "tiempo" transcurrido.
        {
            feuler(x,y,&xaux,&yaux);

            x=xaux;
            y=yaux;

            V=Cyx*x-Cyy*log(x)+Cxy*y-Cxx*log(y);

            fprintf(f,"%lf\t%lf\t%lf\t%lf\n",t,x,y,V);

        }

    #else


        for(t=0;t<MAX;t+=dt)
        {

            fverlet(x,y,&xaux,&yaux);

            x=xaux;
            y=yaux;

            V=Cyx*x-Cyy*log(x)+Cxy*y-Cxx*log(y):


            fprintf(f,"%lf\t%lf\t%lf\t%lf\n",t,x,y,V);

        }



    #endif

    V=Cyx*x-Cyy*log(x)+Cxy*y-Cxx*log(y);

    printf("V_i=%lf\nV_f=%lf\n",Vaux,V);

    }

    fclose(f);
    return 0;
}


void feuler(double xn,double yn,double *xnext,double *ynext)
    {

    double dx_dt,dy_dt;

    dx_dt=Cxx*xn-Cxy*xn*yn;
    dy_dt=Cyx*xn*yn-Cyy*yn;

    *xnext=xn+dx_dt*dt;
    *ynext=yn+dy_dt*dt;
   
    }

void fverlet(double xn,double yn,double *xnext,double *ynext)
    {
    double dx_dt,dy_dt;
    double dx_dt2,dy_dt2;
    double xmed,ymed;

    dx_dt=Cxx*xn-Cxy*xn*yn;
    dy_dt=Cyx*xn*yn-Cyy*yn;

    dx_dt2=Cxx*dx_dt-Cxy+(dy_dt*xn+yn*dx_dt);
    dy_dt2=Cyx*(dy_dt*xn+yn*dx_dt)-Cyy*dy_dt;

    *xnext=xn+dx_dt*dt+dx_dt2*dt*dt*0.5;
    *ynext=yn+dy_dt*dt+dy_dt2*dt*dt*0.5;

    return;
    }