如何在不使用构建器的情况下延迟自动滚动PageView？

import 'dart:async';
import 'package:flutter/material.dart';

class MyPageView extends StatefulWidget {
  @override
  _MyPageViewState createState() => _MyPageViewState();
}

class _MyPageViewState extends State<MyPageView> {
  PageController _pageController;
  Timer _timer;
  int _currentPage = 0;

  @override
  void initState() {
    super.initState();
    _pageController = PageController(initialPage: _currentPage);
    _startTimer();
  }

  @override
  void dispose() {
    _cancelTimer();
    _pageController.dispose();
    super.dispose();
  }

  void _startTimer() {
    _timer = Timer.periodic(Duration(seconds: 5), (timer) {
      if (_currentPage < 2) {
        _currentPage++;
      } else {
        _currentPage = 0;
      }
      _pageController.animateToPage(
        _currentPage,
        duration: Duration(milliseconds: 500),
        curve: Curves.ease,
      );
    });
  }

  void _cancelTimer() {
    _timer?.cancel();
  }

  @override
  Widget build(BuildContext context) {
    return PageView(
      controller: _pageController,
      children: [
        // 页面1
        Container(
          color: Colors.blue,
          child: Center(
            child: Text(
              'Page 1',
              style: TextStyle(fontSize: 24, color: Colors.white),
            ),
          ),
        ),
        // 页面2
        Container(
          color: Colors.red,
          child: Center(
            child: Text(
              'Page 2',
              style: TextStyle(fontSize: 24, color: Colors.white),
            ),
          ),
        ),
        // 页面3
        Container(
          color: Colors.green,
          child: Center(
            child: Text(
              'Page 3',
              style: TextStyle(fontSize: 24, color: Colors.white),
            ),
          ),
        ),
      ],
    );
  }
}