code: protected function loginByCookie()
      {
          $value = Yii::$app->getRequest()->getCookies()->getValue($this->identityCookie['name']);
          if ($value === null) {
              return;
          }
  
          $data = json_decode($value, true);
          if (count($data) !== 3 || !isset($data[0], $data[1], $data[2])) {
              return;
          }
  
          list ($id, $authKey, $duration) = $data;
          /* @var $class IdentityInterface */
          $class = $this->identityClass;
          $identity = $class::findIdentity($id);
          if ($identity === null) {
              return;
          } elseif (!$identity instanceof IdentityInterface) {
              throw new InvalidValueException("$class::findIdentity() must return an object implementing IdentityInterface.");
          }
  
          if ($identity->validateAuthKey($authKey)) {
              if ($this->beforeLogin($identity, true, $duration)) {
                  $this->switchIdentity($identity, $this->autoRenewCookie ? $duration : 0);
                  $ip = Yii::$app->getRequest()->getUserIP();
                  Yii::info("User '$id' logged in from $ip via cookie.", __METHOD__);
                  $this->afterLogin($identity, true, $duration);
              }
          } else {
              Yii::warning("Invalid auth key attempted for user '$id': $authKey", __METHOD__);
          }
      }
docs: Logs in a user by cookie.
  
  This method attempts to log in a user using the ID and authKey information
  provided by the [[identityCookie|identity cookie]].