下面的代码将动画的宽度的边界

class Test extends StatefulWidget {
  @override
  _TestState createState() => _TestState();
}

class _TestState extends State<Test> with TickerProviderStateMixin {

  AnimationController _resizableController;

  AnimatedBuilder getContainer() {
    return new AnimatedBuilder(
        animation: _resizableController,
        builder: (context, child) {
          return Container(
            padding: EdgeInsets.all(24),
            child: Text("SAMPLE"),
            decoration: BoxDecoration(
              shape: BoxShape.rectangle,
              borderRadius: BorderRadius.all(Radius.circular(12)),
              border: Border.all(
                  color: Colors.blue, width: _resizableController.value * 10),
            ),
          );
        });
  }

  @override
  void initState() {
    _resizableController = new AnimationController(
      vsync: this,
      duration: new Duration(
        milliseconds: 1000,
      ),
    );
    _resizableController.addStatusListener((animationStatus) {
      switch (animationStatus) {
        case AnimationStatus.completed:
          _resizableController.reverse();
          break;
        case AnimationStatus.dismissed:
          _resizableController.forward();
          break;
        case AnimationStatus.forward:
          break;
        case AnimationStatus.reverse:
          break;
      }
    });
    _resizableController.forward();
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
        backgroundColor: Colors.white,
        appBar: AppBar(
          title: Text("Test"),
          centerTitle: true,
        ),
        body: Center(child: getContainer()));
  }
}

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的数据

感谢Lakhwinder Singh，我做了这个代码，它做了我要求的发光效果：

import 'package:flutter/material.dart';

void main()  {
  runApp(new Test());
}

class Test extends StatefulWidget {
  @override
  _TestState createState() => _TestState();
}

class _TestState extends State<Test> with TickerProviderStateMixin {

  AnimationController _resizableController;

  static Color colorVariation(int note){
    if(note <= 1){
      return Colors.blue[50];
    }else if(note>1 && note<=2){
      return Colors.blue[100];
    }else if(note>2 && note<=3){
      return Colors.blue[200];
    }else if(note>3 && note<=4){
      return Colors.blue[300];
    }else if(note>4 && note<=5){
      return Colors.blue[400];
    }else if(note>5 && note<=6){
      return Colors.blue;
    }else if(note>6 && note<=7){
      return Colors.blue[600];
    }else if(note>7 && note<=8){
      return Colors.blue[700];
    }else if(note>8 && note<=9){
      return Colors.blue[800];
    }else if(note>9 && note<=10){
      return Colors.blue[900];
    }
  }

  AnimatedBuilder getContainer() {
    return new AnimatedBuilder(
        animation: _resizableController,
        builder: (context, child) {
          return Container(
            //color: colorVariation((_resizableController.value *100).round()),
            padding: EdgeInsets.all(24),
            child: Text("SAMPLE"),
            decoration: BoxDecoration(
              shape: BoxShape.rectangle,
              borderRadius: BorderRadius.all(Radius.circular(12)),
              border: Border.all(
                  color: colorVariation((_resizableController.value *10).round()), width:10),
            ),
          );
        });
  }

  @override
  void initState() {
    _resizableController = new AnimationController(
      vsync: this,
      duration: new Duration(
        milliseconds: 500,
      ),
    );
    _resizableController.addStatusListener((animationStatus) {
      switch (animationStatus) {
        case AnimationStatus.completed:
          _resizableController.reverse();
          break;
        case AnimationStatus.dismissed:
          _resizableController.forward();
          break;
        case AnimationStatus.forward:
          break;
        case AnimationStatus.reverse:
          break;
      }
    });
    _resizableController.forward();
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home:Scaffold(
        backgroundColor: Colors.white,
        body: Center(child: getContainer())));
  }
}

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如果您在应用中使用状态管理包，例如Get、Provider等，则可以使用您可以提供的bool侦听AnimationContiner。
假设您有一个名为isEmptyError的bool变量，如下所示

final isEmptyError = false.obs;

Obx(
      () => AnimatedContainer(
        duration: const Duration(seconds: 1),
        curve: Curves.fastOutSlowIn,
        decoration: BoxDecoration(
          border: Border.all(
            color: Get.theme.primaryColor,
            width: 6,
            style: isEmptyError() ? BorderStyle.solid : BorderStyle.none,
          ),
        ),
        child: TextButton(
            style: ButtonStyle(overlayColor: MaterialStateColor.resolveWith((_) => Colors.transparent)),
            child: const Text('Press To Flash'),
            onPressed: () {
              isEmptyError(true);
              Future.delayed(const Duration(milliseconds: 300), () => isEmptyError(false));
              Future.delayed(const Duration(milliseconds: 600), () => isEmptyError(true));
              Future.delayed(const Duration(milliseconds: 900), () => isEmptyError(false));
            },
        ),
      ),
    ),

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我发现将AnimatedContainer与Timer一起使用最简单。
下面是一个完整的工作示例：https://dartpad.dev/010e8a96bae7cd84375c087cc06c11d3

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

class AnimatedBorderComponent extends StatefulWidget {
  const AnimatedBorderComponent({ super.key });

  @override
  State<AnimatedBorderComponent> createState() { return _AnimatedBorderComponentState(); }
}

class _AnimatedBorderComponentState extends State<AnimatedBorderComponent> { 
  int index = 0;
  List<Color> colors = [Colors.red, Colors.orange, Colors.yellow, Colors.green, Colors.blue, Colors.purple];
  Duration duration = const Duration(milliseconds: 250);
  Timer? _timer;

  @override
  void initState() {
    super.initState();

    // set up a timer, make state changes, and redraw.
    _timer = Timer.periodic(duration, (timer) {
      index = (index + 1) % colors.length;
      if (mounted) { setState(() {}); }
    });
  }

  @override
  void dispose() {
    super.dispose();

    // make sure to dispose of the timer when you're done.
    _timer?.cancel();
  }

  @override
  Widget build(BuildContext context) {
    return AnimatedContainer(
      duration: duration,
      curve: Curves.easeInOut,

      // change whatever properties you want, and the
      // AnimatedContainer takes care of the heavy lifting.
      decoration: BoxDecoration(
        border: Border.all(color: colors[index], style: BorderStyle.solid, width: 4),
      ),
    );
  }
}

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根据AaronScherbing的回答，总是在处理小部件之前取消东西