%?=========================================================================
%?Matlab?program?to?draw?a?phase?portrait?for?the?LotkaVolterra?Predetor
%?Pey?model.?The?results?are?shown?at?each?time?step.?
%?In?addition?the?user?has?the?option?of?plotting?a?time?series?graph?for?x?or?y.?
%?Set?the?parameter?choice?=?1?for?a?time?series?plot?for?x.
%?Set?choice?=?2?for?a?time?series?plot?for?y.?
%?Equation?parameters?alpha?beta?gamma?and?detla?can?be?changed?by?the
%?user.
%?Equations?are?solved?using?a?numerical?ODE?solver.?
%
%?James?Adams?3/4/14
%?=========================================================================

function?LotkaVolterra_JA
clear??%?Clears?command?window
clc????%?Clears?command?history
clf????%?Removes?anything?in?the?figure?window?before?simulation.?

%?===============?Set?choice?to?1?or?2?====================================?
choice?=?2;??

countdown?=?5;??%?Countdown?time?length?before?simulation?runs.?
iterations?=?1;??%?Sets?initial?interation?count?to?1;
pausetime?=?0.1;??%?Shows?solutions?at?each?time?step.?
runtime?=?10;????%?Duration?time?of?simulation.

%?================?Equation?parameter?values?==============================
alpha?=?1;
beta?=?8/3;
gamma?=?1;
delta?=?1;

%?===============?Initial?conditions?for?x?and?y?==========================
initialx?=?1;
initialy?=?1;

fprintf（‘----------------------------------\nLotkaVolterra?Predetor?Prey?model?\n\nMatlab?code?written?by?James?Adams\n----------------------------------‘）
fprintf（‘\n\nParameter?values?set‘）
fprintf（‘\n\nalpha?=?%2.6f?\nbeta?=?%2.6f?\ngamma?=?%2.6f?\ndelta?=?%2.6f?‘alphabetagammadelta）
fprintf（‘\n\nTo?plot?a?time?series?graph?for?x?set?the?choice?parameter?in?the?code?to?1.‘）?
fprintf（‘\nSet?choice?to?2?to?plot?a?time?series?graph?for?y.\n\nSimulation?will?run?in?‘）

for?i?=?5:-1:1
????fprintf（‘\n%8i‘countdown‘）????%?Countdown?to?simulation?start.
????countdown?=?countdown-1;
????pause（1）
end

%?Solves?equations?using?numerical?ODE?solver?45?（nonstiff?runge?kutta）
deq1=@（tx）?[x（1）*（alpha?-?beta*x（2））;?-x（2）*（gamma-delta*x（1））];
[tsol]?=?ode45（deq1[0?runtime][initialx?initialy]）;

arraysize?=?size（t）;??%?Sets?time?array?size?for?the?for?loop.

%============?Solutions?are?plotted?at?each?time?step?=====================

for?i?=?1?:?max（arraysize）?
????subplot（211）
????plot（sol（iterations1）sol（iterations2）‘.‘‘color‘[rand;?rand;?rand]‘markersize‘14‘MarkerFaceColor‘‘b‘）;???????????????????????????????
????hold?on
????title（[‘Lotka-Volterra?Equations???????t?=?‘?num2str（t（iterations））]‘fontsize‘12）
????xlabel（‘x‘‘fontsize‘12）
????ylabel（‘y‘‘fontsize‘12）
????axis（[min（sol（:1））?max（sol（:1））?min（sol（:2））?max（sol（:2））]）
????
????subplot（212）
????text（0.10.5‘Time?Series?graph?will?be?shown?at?the?end?of?the?simulation‘）
????
????iterations?=?iterations?+?1;???%?Adds?1?to?the?iteration?count.?
????pause（pausetime）
end

%?====?Plots?time?series

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3882??2014-10-02?18:18??LotkaVolterra_JA.m
?????文件????????1311??2014-10-02?18:18??license.txt