How to use ode 45 to solve a system that is piecewise continous

I am trying to use ode45 to solve a differential equation in which a parameter depends on time. When t is even the parameter is zero and 'a' for odd case. I wrote two functions F1 and F2, that represented my system with and without the parameter a. I tried to use the if statement inside a for loop to execute ode

x=[0 1]'

for t=0:0.01:100
 z=t/2;
if z-floor(z) = 0 
ode = @(t,x)F1(t,x);
  [t,x]=ode45(ode,t,x);
else
ode = @(t,x)F2(t,x);
  [t,x]=ode45(ode,t,x);
end

 end
(plot(x(:,1),x(:,2)))

 how do i make sure that output of at t=1 is taken as input at t=2 as the system parameter alternate