Flutter : how to actualize the state of a global variable in every widget?

Question

so i have 2 pages and 1 file where i have my variable . when i run the app my variable total is update every time i enter income page or add a new income . but when i navigate back to the home page the total shows only the first value ive entered .
Home.dart

import 'package:flutter/material.dart';
import 'componets.dart';
import 'income.dart';
import 'variables.dart';
....
bottomNavigationBar: Container(
        color: Colors.white,
        child: Row(
          children: <Widget>[
            Expanded(
              child: ListTile(
                title: new Text("Balance:"),
                subtitle: new Text("$Total"),
              ),
            ),

the variable total is shown in the bottom of home page

Income.dart

import 'package:flutter/material.dart';
import 'componets.dart';
import 'home.dart';
import 'variables.dart';

class Income extends StatefulWidget {
  const Income({Key? key}) : super(key: key);

  @override
  State<Income> createState() => _IncomeState();
}

class _IncomeState extends State<Income> {
  TextEditingController _textFieldController = TextEditingController();
  List<double> transactions = [];

  Future<void> _displayTextInputDialog(BuildContext context) async {
    double Amount = 0;
    String valueText = '';
    return showDialog(
        context: context,
        builder: (context) {
          return AlertDialog(
            title: Text('Add income'),
            content: TextField(
              keyboardType: TextInputType.number,
              onChanged: (value) {
                setState(() {
                  valueText = value;
                });
              },
              controller: _textFieldController,
            ),
            actions: <Widget>[
              FlatButton(
                color: Colors.red,
                textColor: Colors.white,
                child: Text('CANCEL'),
                onPressed: () {
                  setState(() {
                    Navigator.pop(context);
                  });
                },
              ),
              FlatButton(
                color: Colors.green,
                textColor: Colors.white,
                child: Text('OK'),
                onPressed: () {
                  setState(() {
                    Amount = double.parse(valueText);
                    transactions.add(Amount);
                    Total = Total + Amount;
                    print(Amount);
                    Navigator.pop(context);
                  });
                },
              ),
            ],
          );
        });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Income"),
        backgroundColor: Colors.deepOrange,
        centerTitle: false,
        elevation: 1.0,
      ),
      body: Center(
        child: FlatButton(
          color: Colors.teal,
          textColor: Colors.white,
          onPressed: () {
            _displayTextInputDialog(context);
          },
          child: Text('Press For Alert'),
        ),
      ),

//      NavigationBar
      bottomNavigationBar: Container(
        color: Colors.white,
        child: Row(
          children: <Widget>[
            Expanded(
              child: ListTile(
                title: Text("Balance:"),
                subtitle: Text('${Total}'),
              ),
            ),

the variable in the same place as the home page variables.dart

double Total = 0;

Answer 1

I have created example of updating total value using provider by refering yours

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


//Provider for updating totalvalue
class TotalValue with ChangeNotifier {
double _total = 0;

double get value => _total;

void sum(double val) {
 _total += val;
 notifyListeners();
 }
}

//Income Page
class Income extends StatefulWidget {
const Income({Key? key}) : super(key: key);

@override
State<Income> createState() => _IncomeState();
}

class _IncomeState extends State<Income> {
TextEditingController _textFieldController = TextEditingController();
List<double> transactions = [];

Future<void> _displayTextInputDialog(BuildContext context) async {
  double Amount = 0;
  String valueText = '';
  return showDialog(
    context: context,
    builder: (context) {
      return AlertDialog(
        title: Text('Add income'),
        content: TextField(
          keyboardType: TextInputType.number,
          onChanged: (value) {
            setState(() {
              valueText = value;
            });
          },
          controller: _textFieldController,
        ),
        actions: <Widget>[
          FlatButton(
            color: Colors.red,
            textColor: Colors.white,
            child: Text('CANCEL'),
            onPressed: () {
              Navigator.pop(context);
            },
          ),
          FlatButton(
            color: Colors.green,
            textColor: Colors.white,
            child: Text('OK'),
            onPressed: () {
              Amount = double.parse(valueText);
              transactions.add(Amount);
              context.read<TotalValue>().sum(Amount);
              Navigator.pop(context);
            },
          ),
        ],
      );
    });
}

@override
 Widget build(BuildContext context) {
  return Center(
   child: FlatButton(
    color: Colors.teal,
    textColor: Colors.white,
    onPressed: () {
      _displayTextInputDialog(context);
     },
     child: Text('Press For Alert'),
    ),
  );
 }
}

//Home Page
class Home extends StatefulWidget {
const Home({Key? key}) : super(key: key);

@override
State<Home> createState() => _HomeState();
}

class _HomeState extends State<Home> {
 int _selectedIndex = 0;
 static TextStyle optionStyle =
 TextStyle(fontSize: 30, fontWeight: FontWeight.bold);
 static List<Widget> _widgetOptions(BuildContext context) {
   return <Widget>[
     Income(),
     Text(
      '${context.watch<TotalValue>().value}',
      style: optionStyle,
     ),
  ];
 }

 void _onItemTapped(int index) {
   setState(() {
   _selectedIndex = index;
  });
 }

 @override
 Widget build(BuildContext context) {
  return Scaffold(
    appBar: AppBar(
    title: const Text('Income'),
  ),
  body: Center(
    child: _widgetOptions(context).elementAt(_selectedIndex),
  ),
  bottomNavigationBar: BottomNavigationBar(
    items: const <BottomNavigationBarItem>[
      BottomNavigationBarItem(
        icon: Icon(Icons.home),
        label: 'Home',
      ),
      BottomNavigationBarItem(
        icon: Icon(Icons.money),
        label: 'Income',
      ),
    ],
     currentIndex: _selectedIndex,
     selectedItemColor: Colors.amber[800],
     onTap: _onItemTapped,
    ),
  );
 }
}