Errors when using ODE 45, Phase portraits

Elina Makieva

2018 11 11

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Hello! Please help me in creating a phase portrait for the system of differential equations. I`ve received such errors:

1) Error using PE>peFun Too many input arguments.

2)Error in odearguments (line 90) f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

3)Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

4) Error in PE (line 15) [tSol,ALPHASol]=ode45(@peFun,tspan,vPUR,vER,ALPHA0); %function calling before function definition

 Sorry I make a mistake in previous code, but still receive errors:
tspan=[0 1];
aplha=[0 pi];
beta=[0 pi];
% To run P-E system
%%Initialization
eta0=pi/4;
r0=sqrt(2);
beta0=0;
alpha0=pi/4;
xP0=0;
yP0=0;
xE0=1;
yE0=1;
ALPHA0=[eta0;r0;beta0;alpha0;xP0;yP0;xE0;yE0];
[tSol,ALPHASol]=ode45(@peFun,tspan,ALPHA0);      
%function calling before function definition
plot(tSol,ALPHASol);
function fval=peFun(t,ALPHA)
% Get variables
eta=ALPHA(1);
r=ALPHA(2);
beta=ALPHA(3);
alpha=ALPHA(4);
xP=ALPHA(5);
yP=ALPHA(6);
xE=ALPHA(7);
yE=ALPHA(8);
% Constants
a=1;
% Describing dALPHA/dt
for alpha=[0 pi];
  beta=[0 pi];
fval=zeros(8,1);
fval(1,1)=(-vPUR*sin(beta)+vER*sin(alpha))/r;
fval(2,1)=vER*cos(alpha)-vPUR*cos(beta);
fval(3,1)=(a/r)*(vER*sin(alpha)-vPUR*sin(beta));
fval(4,1)=(-vER*sin(alpha)+vER*sin(beta))/r;
fval(5,1)=vPUR*cos(eta+beta);
fval(6,1)=vPUR*sin(eta+beta);
fval(7,1)=vER*cos(eta+alpha);
fval(8,1)=vER*sin(eta+alpha);
end;
end