Issue with integration tolerances

I am trying to use this code to plot a series of Differential equations in Matlab, and it does give me plots however they are not spanning over the entire boundary of t that I am setting and I am getting this error

Warning: Failure at t=4.470044e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.881784e-16) at time t.

Can anyone explain why this is happening?

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Rudimentary script to solve an initial value problem consisting of the
% following system of two differential equations on the interval a<=t<=b
%
% x1'(t) = alpha*x1+beta*x2, x1(a) = x1_0
% x2'(t) = gamma*x1+delta*x2, x2(a) = x2_0
%
% Look for "*** Your entry i ***" where i=1,2,3,4,5,6 to make appropriate
% changes to solve your specific system
%
% Running the script as is outputs the unit circle as the trajectory with
% x1(t) = cos t and x2(t) = -sin t for the time series
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Housekeeping
clc ; % clear the command window
clear; % clear all variables
close all; % close all figures
% ODE45 options
options = odeset('AbsTol',1e-10,'RelTol',1e-6);
% Independent variable
a = 0; % left endpoint of t interval *** Your entry 1 ***
b = 20; % right endpoint of t interval *** Your entry 2 ***
h = 0.01; % stepsize *** Your entry 3 ***
tt = a:h:b;
% Initial value of dependent variables
x1_0 = 5; % initial value of x1 *** Your entry 4 ***
x2_0 = 1; % initial value of x2 *** Your entry 5 ***
x0 = [x1_0 x2_0];
% Solve the system
[t,soln] = ode45(@(t,x) rhs(t,x),tt,x0,options);

Warning: Failure at t=4.474016e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.881784e-16) at time t.

% Plot solutions
figure(1); % time series of x1(t)
plot(t,soln(:,1));
xlabel('$t$','Interpreter','latex','FontSize',20);
ylabel('$x_1$','Interpreter','latex','FontSize',20,'Rotation',0)
grid on

●

figure(2); % time series of x2(t)
plot(t,soln(:,2));
xlabel('$t$','Interpreter','latex','FontSize',20);
ylabel('$x_2$','Interpreter','latex','FontSize',20,'Rotation',0);
grid on

figure(3); % phase portrait
plot(soln(:,1),soln(:,2));
xlabel('$x_1$','Interpreter','latex','FontSize',20);
ylabel('$x_2$','Interpreter','latex','FontSize',20,'Rotation',0)
grid on
axis square

% Right hand side of the system differential equations
function [xp] = rhs(t,x) % do not change this line
% *** Your entry 6 *** (start entering your system here)
alpha = 1.5;
beta = 1.1;
gamma = 2.5;
delta = 1.4;
x1prime = -alpha*x(1) + beta*x(1)*x(2);
x2prime = gamma*x(2)*(1-0.5*x(2)) + delta*x(1)*x(2);
% *** Your entry 6 *** (stop entering your system here)
xp = [x1prime ; x2prime]; % do not change this line
end % do not change this line

[Torsten]

Most probably, the solution to your ODE system has a singularity at t = 0.4474 ... (like tan(t) blows up at t = pi/2, e.g.) .

[Walter Roberson]

I tried it symbolically, taking the given equations and using dsolve()... it said that it could not find the answer.