//***********************************************************************************
/** Class to return iterate of Duffing map function.<br>
*/
//***********************************************************************************

public class DuffingMapFunction extends Map2DFunction {
      double X,Y;

      DuffingMapFunction() {      

            nParameters=2;    
            a = new double[nParameters];    
            aDefault = new double[nParameters];
            aDefault[0]=2.75;
            aDefault[1]=0.2;      
            title = "Duffing Map";
            xminDefault=-2.0;
            xmaxDefault=2.0;
            yminDefault=-2.0; 
            ymaxDefault=2.0;
      }      
                       
      
//***********************************************************************************      
/** iterates the map function
* @param x input value
* @return iterated value
*/
//***********************************************************************************
      public void iterate(double[] x) {                       

            X = x[0];
            Y = x[1];

            x[0] = Y; 
            x[1] = -a[1]*X+a[0]*Y-Y*Y*Y;
            
            x[2]=X;
            x[3]=Y; 
      }      

//***********************************************************************************      
/** iterates the tangent space to the map
* @param x input value and returns updated values
* x[0] and x[1] contain the new values of X and Y
* x[2] and x[3] contain the previous values
* @param t value of tangent vector (updated by iteration)
*/
//***********************************************************************************
      public void iterateTangent(double[] x, double[] t) {             
      
      X = t[0];
      Y = t[1];
      t[0] = Y;
      t[1] = -a[1]*X+a[0]*Y-3*x[1]*x[1]*Y;
      
      }   
//***********************************************************************************               
}