How to take a point (xn, yn) in the plane and maps it to a new point?

I tried to use the loop method but the program stuck.

function getPoints() {
  var x, y;

  for (
    x = 1, y = 2, a = 1.4, b = 0.3;
    x < 10, y < 10;
    x = 1 - a * x ** 2 + y, y = b * x
  ) {
    console.log(x, y);
  }
}

> I would like to see how this system works and get a list with points (x,y) after a few iterations.

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function getPoints() {
  const a = 1.4,
    b = 0.3
  for (
    let i = 0, x = 1, y = 2; i < 10; i += 1
  ) {
    x = 1 - a * x ** 2 + y
    y = b * x
    console.log(x, y);
  }
}

getPoints()

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As Konrad pointed out in a comment, x and y become negative and never again become positive, so the loop never ends. In this case, a better solution would be to use a while-loop and check for the absolute value of x and y, so the loop will terminate regardless of what direction the values go:

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let x = 1, y = 2
const a = 1.4, b = 0.3;

while (Math.abs(x) < 10 && Math.abs(y) < 10) {
  console.log(x, y)
  x = 1 - a * x ** 2 + y;
  y = b * x;
}

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Also, note that your original for-loop does not do what you think it does. In the expression x < 10, y < 10, the comma does not mean and, it is a comma operator and means forget everything except the thing after the last comma, which is y < 10. Expand the snippet below to see an example.

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for (
  let a = 0, b = 0;
  a < 10, b < 10;
  a += 2, b++
  ) {
  console.log(a, b)
  }

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