欢迎来到海神之光博客之家✅博主简介热爱科研的Matlab仿真开发者修心和技术同步精进个人主页海神之光代码获取方式海神之光Matlab王者学习之路—代码获取方式⛳️座右铭行百里者半于九十。更多Matlab元胞自动机仿真内容点击①Matlab元胞自动机进阶版⛳️关注CSDN海神之光更多资源等你来⛄一、元胞自动机简介1 元胞自动机发展历程最初的元胞自动机是由冯 · 诺依曼在 1950 年代为模拟生物 细胞的自我复制而提出的. 但是并未受到学术界重视.1970 年, 剑桥大学的约翰 · 何顿 · 康威设计了一个电脑游戏 “生命游戏” 后, 元胞自动机才吸引了科学家们的注意.1983 年 S.Wolfram 发表了一系列论文. 对初等元胞机 256 种 规则所产生的模型进行了深入研究, 并用熵来描述其演化行 为, 将细胞自动机分为平稳型, 周期型, 混沌型和复杂型.2 对元胞自动机的初步认识元胞自动机CA是一种用来仿真局部规则和局部联系的方法。典型的元胞自动机是定义在网格上的每一个点上的网格代表一个元胞与一种有限的状态。变化规则适用于每一个元胞并且同时进行。典型的变化规则决定于元胞的状态以及其 4 或 8 邻居的状态。3 元胞的变化规则元胞状态典型的变化规则决定于元胞的状态以及其 4 或 8 邻居的状态。4 元胞自动机的应用元胞自动机已被应用于物理模拟生物模拟等领域。5 元胞自动机的matlab编程结合以上我们可以理解元胞自动机仿真需要理解三点。一是元胞在matlab中可以理解为矩阵中的一点或多点组成的方形块一般我们用矩阵中的一点代表一个元胞。二是变化规则元胞的变化规则决定元胞下一刻的状态。三是元胞的状态元胞的状态是自定义的通常是对立的状态比如生物的存活状态或死亡状态红灯或绿灯该点有障碍物或者没有障碍物等等。6 一维元胞自动机——交通规则定义6.1 元胞分布于一维线性网格上.6.2 元胞仅具有车和空两种状态.7 二维元胞自动机——生命游戏定义7.1 元胞分布于二维方型网格上.7.2 元胞仅具有生和死两种状态.元胞状态由周围八邻居决定.规则骷髅死亡笑脸生存周围有三个笑脸则中间变为笑脸少于两个笑脸或者多于三个中间则变死亡。8 什么是元胞自动机离散的系统: 元胞是定义在有限的时间和空间上的, 并且元 胞的状态是有限.动力学系统: 元胞自动机的举止行为具有动力学特征.简单与复杂: 元胞自动机用简单规则控制相互作用的元胞 模拟复杂世界.9 构成要素1元胞 (Cell)元胞是元胞自动机基本单元状态: 每一个元胞都有记忆贮存状态的功能.离散: 简单情况下, 元胞只有两种可能状态; 较复杂情况下, 元胞具有多种状态.更新: 元胞的状态都安照动力规则不断更新.2网格 (Lattice)不同维网格常用二维网格3邻居 (Neighborhood)4边界 (Boundary)反射型以自己作为边界的状态吸收型不管边界车开到边界就消失5规则状态转移函数定义根据元胞当前状态及其邻居状况确定下一时刻该元胞状态的动力学函数, 简单讲, 就是一个状态转移函数.分类 总和型: 某元胞下时刻的状态取决于且仅取决于它所有邻居 的当前状态以及自身的当前状态.合法型: 总和型规则属于合法型规则. 但如果把元胞自动机 的规则限制为总和型, 会使元胞自动机具有局限性.6森林火灾绿色树木红色火黑色空地。三种状态循环转化树周围有火或者被闪电击中就变成火。空地以概率p变为树木理性分析红为火灰为空地绿是树元胞三种状态的密度和为1火转化为空地的密度等于空地转换为树的密度新长出来的树等于烧没的树f是闪电的概率:远远小于树生成的概率T s m a x T_{smax}T smax​是一大群树被火烧的时间尺度程序实现周期性边界条件购进啊其中的数字为编号构建邻居矩阵上面矩阵中的数字编号对应原矩阵相同位置编号的上邻居编号一 一对应同样道理7交通概念车距和密度流量方程守恒方程时空轨迹横轴是空间纵轴为时间红线横线与蓝色交点表示每个时间车的位置。如果是竖线则表示车子在该位置对应的时间宏观连续模型最常用的规则红色条表示速度是满的。1 加速规则不能超过v m a x 2 格 / s v_{max}2格/svmax2格/s2 防止碰撞不能超过车距理论分析结果分析: 密度与流量第一个图横坐标是归一化后的密度纵坐标是车流量。第二个图理论值与CA的结果结果分析: 时空轨迹中间的深色区域是交通堵塞的区域。⛄二、部分源代码%% NOTE% Total runtime for this code was about 7.5 hours on the computer used by% the original researcher (for 1000 run average of 3 different adherence% values).% This runtime is expected to vary from device to device, and is being used% here to obtain a general comparison for runtime for the different% models. It is not for a universal runtime value% When run, this code does not display anything at the beginning. However,% it will produce 2 graphs for each P_adh value every 2.5 hours approx.%% Documentation% n size of each dimension of our square cellular automata grid% P_HIV fraction (probability) of cells initially infected by virus% P_i probability of a healthy cell becoming infected if its% neighborhood contains 1 I1 cell or X I2 cells% P_v probability of a healthy cell becoming infected by coming% in contact with a virus randomly (not from its% neighborhood)% P_RH Probability of a dead cell becoming replaced by a healthy% cell% P_RI Probability of a dead cell becoming replaced by an infected% cell% P_T1 Probability of a healthy cell receiving therapy 1% P_iT1 Probability of a healthy cell receiving therapy 1 of% becoming infected% P_T2 Probability of a healthy cell receiving therapy 2% P_iT2 Probability of a healthy cell receiving therapy 2 of% becoming infected% X Number of I2 cells in the neighborhood of an H cell that% can cause it to become infected% tau1 tau1 is the number of timesteps it takes for an acute% infected cell to become latent.% tau2 tau2 is the number of timesteps it takes for a latent% infected cell to become dead.% tau3 tau3 is the number of timesteps after which a healthy% cell receiving dual therapy becomes a healthy cell again% totalsteps totalsteps is the total number of steps of the CA (the% total number of weeks of simulations)% grid our cellular automata (CA) grid% tempgrid tempgrid is a temporary grid full of random numbers that is% used to randomly add different states to our CA grid.% taugrid taugrid is a grid the same size as our CA grid that stores% the number of timesteps that a cell has been in state I_1.% If the number reaches tau1, then the state changes to I_2.% state state is a [9 x totalsteps] size matrix that stores% the total number of cells in each state at each timestep% and the last 2 rows store total healthy and total infected% cells% timestep each simulation step of the cellular automata% 1 timestep 1 week of time in the real world% nextgrid nextgrid is a temporary grid. It is a copy of the CA grid% from the previous simulation. It stores all the CA rule% updates of the current timestep and stores it all back to% the grid to display.%% Clean-upclc; % clears command windowclear all; % clears workspace and deletes all variables% close all; % closes all open figures%% Parametersn 100; % meaning that our grid will have the dimensions n x nP_HIV 0.05; % initial grid will have P_hiv acute infected cellsP_i 0.997; % probability of infection by neighborsP_v 0.00001; % probability of infection by random viral contactP_RH 0.99; % probability of dead cell being replaced by healthyP_RI 0.00001; % probability of dead cell being replaced by infectedP_T1 0.70; % probability of cell receiving therapy 1P_iT1 0.07; % probability of infection of healthy with therapy 1P_T2 0.50; % probability of cell receiving therapy 2P_iT2 0.05; % probability of infection of healthy with therapy 2X 4; % there must be at least X I_2 neighbors to infect celltau1 4; % time delay for I_1 cell to become I_2 celltau2 1; % time delay for I_2 cell to become D celltau3 1; % time delay for H_Tb cell to become H celltotalsteps 600; % total number of weeks of simulation to be performedT_start 20; % The medication therapy will start on week T_starttotalruns 1000; % total number of times to run the simulation to get an% average%% States% State 1: H: Healthy (Color- Green)% State 2: H_T1: Healthy with therapy 1 (Color- Red)% State 3: H_T2: Healthy with therapy 2 (Color- Red)% State 4: H_Tb: Healthy with dual therapy (Color- Red)% State 5: I_1: Active Infected (Color- Cyan)% State 6: I_2: Latent Infected (Color- Blue)% State 7: D: Dead (Color- Black)%% Simulationfor P_adh 0.5:0.2:0.9state1 zeros(totalruns,totalsteps); state2 zeros(totalruns,totalsteps); state3 zeros(totalruns,totalsteps); state4 zeros(totalruns,totalsteps); state5 zeros(totalruns,totalsteps); state6 zeros(totalruns,totalsteps); state7 zeros(totalruns,totalsteps); for run 1:totalruns state1dev std(state1); state2dev std(state2); state3dev std(state3); state4dev std(state4); state5dev std(state5); state6dev std(state6); state7dev std(state7); state8dev state1dev state2dev state3dev state4dev; state9dev state5dev state6dev; state1mean mean(state1); state2mean mean(state2); state3mean mean(state3); state4mean mean(state4); state5mean mean(state5); state6mean mean(state6); state7mean mean(state7); state8mean state1mean state2mean state3mean state4mean; state9mean state5mean state6mean; % The following lines of code are to display a graph of each state of % cells during simulation set(figure, OuterPosition, [200 100 700 500]) % sets figure window size plot( 1:totalsteps , state1mean, g, ... 1:totalsteps , state2mean, r, ... 1:totalsteps , state3mean, m, ... 1:totalsteps , state4mean, y, ... 1:totalsteps , state5mean, c, ... 1:totalsteps , state6mean, b, ... 1:totalsteps , state7mean, k , linewidth, 2 ); xlim([0 600]); ylim([0 10000]); hold on; gridxy(20,Color,[0.8 0.5 0.0],linewidth,5) ; errorbar( 1:15:totalsteps , state1mean(1:15:totalsteps), state1dev(1:15:totalsteps), g); errorbar( 1:15:totalsteps , state2mean(1:15:totalsteps), state2dev(1:15:totalsteps), r); errorbar( 1:15:totalsteps , state3mean(1:15:totalsteps), state3dev(1:15:totalsteps), m); errorbar( 1:15:totalsteps , state4mean(1:15:totalsteps), state4dev(1:15:totalsteps), y); errorbar( 1:15:totalsteps , state5mean(1:15:totalsteps), state5dev(1:15:totalsteps), c); errorbar( 1:15:totalsteps , state6mean(1:15:totalsteps), state6dev(1:15:totalsteps), b); errorbar( 1:15:totalsteps , state7mean(1:15:totalsteps), state7dev(1:15:totalsteps), k); legend( Therapy start week, Healthy, Healthy with Therapy1, Healthy with Therapy2, ... Healthy with dual Therapy, Acute Infected, Latent Infected, ... Dead, Location ,NorthEast ); saveas(gcf,strcat(Model3withAdherencePadh,num2str(P_adh*100),Graph1.pdf)); % The following lines of code are to display a graph of each state of % cells during simulation set(figure, OuterPosition, [200 100 700 500]) % sets figure window size plot( 1:totalsteps , state8mean, g, ... 1:totalsteps , state9mean, b, ... 1:totalsteps , state7mean, k , linewidth, 2 ); xlim([0 600]); ylim([0 10000]); hold on; gridxy(20,Color,[0.8 0.5 0.0],linewidth,5) ; errorbar( 1:15:totalsteps , state8mean(1:15:totalsteps), state8dev(1:15:totalsteps), g); errorbar( 1:15:totalsteps , state9mean(1:15:totalsteps), state9dev(1:15:totalsteps), b); errorbar( 1:15:totalsteps , state7mean(1:15:totalsteps), state7dev(1:15:totalsteps), k); legend( Therapy start week, Healthy, Infected, Dead, ... Location ,NorthEast ); saveas(gcf,strcat(Model3withAdherencePadh,num2str(P_adh*100),Graph2.pdf));end⛄三、运行结果⛄四、matlab版本及参考文献1 matlab版本2014a2 参考文献[1]党珊,蒋太刚,巫承军.基于元胞自动机方法的消防疏散仿真研究[J].现代电子技术. 2022,45(21)[2]帅斌,秦梦瑶,许旻昊.基于元胞自动机的高速铁路列车运行仿真研究[J].计算机仿真. 2022,39(08)[3]张睿洋.元胞自动机在两类传染病模型中的应用[J].现代信息科技. 2022,6(10)3 备注简介此部分摘自互联网仅供参考若侵权请联系删除 仿真咨询1 各类智能优化算法改进及应用生产调度、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、公交排班优化、充电桩布局优化、车间布局优化、集装箱船配载优化、水泵组合优化、解医疗资源分配优化、设施布局优化、可视域基站和无人机选址优化2 机器学习和深度学习方面卷积神经网络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、XGBOOST、TCN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3 图像处理方面图像识别、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4 路径规划方面旅行商问题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、天线线性阵列分布优化、车间布局优化5 无人机应用方面无人机路径规划、无人机控制、无人机编队、无人机协同、无人机任务分配6 无线传感器定位及布局方面传感器部署优化、通信协议优化、路由优化、目标定位优化、Dv-Hop定位优化、Leach协议优化、WSN覆盖优化、组播优化、RSSI定位优化7 信号处理方面信号识别、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、信号配时优化8 电力系统方面微电网优化、无功优化、配电网重构、储能配置9 元胞自动机方面交通流 人群疏散 病毒扩散 晶体生长10 雷达方面卡尔曼滤波跟踪、航迹关联、航迹融合