基于MATLAB设计Logistic映射附分叉图

✅作者简介：热爱科研的Matlab仿真开发者，修心和技术同步精进，matlab项目合作可私信。

🍎个人主页：Matlab科研工作室

🍊个人信条：格物致知。

更多Matlab仿真内容点击👇

智能优化算法       神经网络预测       雷达通信      无线传感器        电力系统

信号处理              图像处理               路径规划       元胞自动机        无人机

⛄ 内容介绍

1 算法原理

Logistic映射，也称为Logistic函数或Logistic方程，是一个常用的非线性映射函数，用于将输入映射到区间(0, 1)之间。它的形式如下：

f(x) = 1 / (1 + exp(-x))

在Logistic映射中，x是输入值，exp表示自然指数函数（e的幂），f(x)是映射结果。

Logistic映射具有以下特点：

1. S形曲线：Logistic映射产生的曲线形状呈现S形，从渐进视角而言，当x趋近正无穷时，f(x)趋近于1，当x趋近负无穷时，f(x)趋近于0。
   
2. 非线性变换：Logistic映射是一种非线性变换函数，能够对输入进行非线性映射。与线性函数不同，Logistic映射引入了非线性因素，可以更好地模拟复杂的关系和行为。
   
3. 限制输出范围：Logistic映射将输入限制在(0, 1)之间，即输出值落在单位间隔内。这种特性使其常用于概率、分类问题以及神经网络等领域中。
   

Logistic映射在应用领域具有广泛的应用，包括但不限于以下几个方面：

1. 生物学模型：Logistic映射在生物学中常用于描述生物种群增长的饱和效应，即当环境资源有限时，种群数量达到一个稳定值。
   
2. 神经网络激活函数：Logistic映射作为神经网络中常用的激活函数之一，用于引入非线性特性，使神经网络能够学习和处理复杂的模式。
   
3. 逻辑回归分类器：Logistic映射被广泛应用于逻辑回归模型中，将输入变量通过Logistic函数映射到(0, 1)的概率值，用于二分类问题的概率估计和决策边界判断。
   

总而言之，Logistic映射是一种常用的非线性函数，具有S形曲线和输出范围限制的特点，适用于多个领域中的非线性建模和数据处理任务。

⛄ 部分代码

function varargout = sch(varargin)

% SCH MATLAB code for sch.fig

%      SCH, by itself, creates a new SCH or raises the existing

%      singleton*.

%

%      H = SCH returns the handle to a new SCH or the handle to

%      the existing singleton*.

%

%      SCH('CALLBACK',hObject,eventData,handles,...) calls the local

%      function named CALLBACK in SCH.M with the given input arguments.

%

%      SCH('Property','Value',...) creates a new SCH or raises the

%      existing singleton*.  Starting from the left, property value pairs are

%      applied to the GUI before sch_OpeningFcn gets called.  An

%      unrecognized property name or invalid value makes property application

%      stop.  All inputs are passed to sch_OpeningFcn via varargin.

%

%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one

%      instance to run (singleton)".

%

% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help sch

% Last Modified by GUIDE v2.5 23-Mar-2011 16:14:23

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name',       mfilename, ...

                  'gui_Singleton',  gui_Singleton, ...

                  'gui_OpeningFcn', @sch_OpeningFcn, ...

                  'gui_OutputFcn',  @sch_OutputFcn, ...

                  'gui_LayoutFcn',  [] , ...

                  'gui_Callback',   []);

if nargin && ischar(varargin{1})

   gui_State.gui_Callback = str2func(varargin{1});

end

if nargout

   [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

   gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before sch is made visible.

function sch_OpeningFcn(hObject, eventdata, handles, varargin)

% This function has no output args, see OutputFcn.

% hObject    handle to figure

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% varargin   command line arguments to sch (see VARARGIN)

% Choose default command line output for sch

handles.output = hObject;

% Update handles structure

guidata(hObject, handles);

% UIWAIT makes sch wait for user response (see UIRESUME)

% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.

function varargout = sch_OutputFcn(hObject, eventdata, handles)

% varargout  cell array for returning output args (see VARARGOUT);

% hObject    handle to figure

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure

varargout{1} = handles.output;

% --- Executes on slider movement.

function slider1_Callback(hObject, eventdata, handles)

% hObject    handle to slider1 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'Value') returns position of slider

%        get(hObject,'Min') and get(hObject,'Max') to determine range of slider

value=get(hObject,'value');

set(handles.edit2,'string',value)

% --- Executes during object creation, after setting all properties.

function slider1_CreateFcn(hObject, eventdata, handles)

% hObject    handle to slider1 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: slider controls usually have a light gray background.

if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

   set(hObject,'BackgroundColor',[.9 .9 .9]);

end

% --- Executes on slider movement.

function slider2_Callback(hObject, eventdata, handles)

% hObject    handle to slider2 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'Value') returns position of slider

%        get(hObject,'Min') and get(hObject,'Max') to determine range of slider

value=get(hObject,'value');

set(handles.edit3,'string',value)

% --- Executes during object creation, after setting all properties.

function slider2_CreateFcn(hObject, eventdata, handles)

% hObject    handle to slider2 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: slider controls usually have a light gray background.

if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

   set(hObject,'BackgroundColor',[.9 .9 .9]);

end

% --- Executes on slider movement.

function slider3_Callback(hObject, eventdata, handles)

% hObject    handle to slider3 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'Value') returns position of slider

%        get(hObject,'Min') and get(hObject,'Max') to determine range of slider

value=get(hObject,'value');

set(handles.edit4,'string',value)

% --- Executes during object creation, after setting all properties.

function slider3_CreateFcn(hObject, eventdata, handles)

% hObject    handle to slider3 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: slider controls usually have a light gray background.

if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

   set(hObject,'BackgroundColor',[.9 .9 .9]);

end

% --- Executes on button press in pushbutton1.

function pushbutton1_Callback(hObject, eventdata, handles)

% hObject    handle to pushbutton1 (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

axes(handles.axes1);

cla;

clear r s x1 y1;

a=get(handles.slider1,'Value');

x=get(handles.slider2,'Value');

n=get(handles.slider3,'Value');

j=get(handles.popupmenu1,'Value');

n=fix(n);

grid off;

⛄ 运行结果

⛄ 参考文献

[1] 李萌,穆秀春.基于混沌序列的图像加密技术[J].黑龙江科技信息, 2008(11):2.DOI:10.3969/j.issn.1673-1328.2008.11.038.

[2] 袁涛,张文瑞,阿依先木·阿洪,等.基于Logistic回归的大学生MATLAB课程成绩的影响因素分析[J].科技视界, 2019.DOI:CNKI:SUN:KJSJ.0.2019-23-049.

🍅 仿真咨询

1.卷积神经网络（CNN）、LSTM、支持向量机（SVM）、最小二乘支持向量机（LSSVM）、极限学习机（ELM）、核极限学习机（KELM）、BP、RBF、宽度学习、DBN、RF、RBF、DELM实现风电预测、光伏预测、电池寿命预测、辐射源识别、交通流预测、负荷预测、股价预测、PM2.5浓度预测、电池健康状态预测、水体光学参数反演、NLOS信号识别、地铁停车精准预测、变压器故障诊断

2.图像识别、图像分割、图像检测、图像隐藏、图像配准、图像拼接、图像融合、图像增强、图像压缩感知

3.旅行商问题（TSP）、车辆路径问题（VRP、MVRP、CVRP、VRPTW等）、无人机三维路径规划、无人机协同、无人机编队、机器人路径规划、栅格地图路径规划、多式联运运输问题、车辆协同无人机路径规划

4.无人机路径规划、无人机控制、无人机编队、无人机协同、无人机任务分配

5.传感器部署优化、通信协议优化、路由优化、目标定位

6.信号识别、信号加密、信号去噪、信号增强、雷达信号处理、信号水印嵌入提取、肌电信号、脑电信号

7.生产调度、经济调度、装配线调度、充电优化、车间调度、发车优化、水库调度、三维装箱、物流选址、货位优化

8.微电网优化、无功优化、配电网重构、储能配置

9.元胞自动机交通流 人群疏散 病毒扩散 晶体生长

⛳️ 代码获取关注我

❤️部分理论引用网络文献，若有侵权联系博主删除

❤️ 关注我领取海量matlab电子书和数学建模资料