property + dynamic response of coupled differential equations

    Hello,
      Here is the typical model I am interested in:
      1. given a set of constants
        a,b,c,d , if needed consider say (1,-1,1,1)
      and initial conditions
          xi, yi (idem, (1,1))
      2. the system of ordinary differential equations
        dx/dt=ax+by
        dy/dt=cx+dy
      and thus the Jacobian matrix for the problem
      [a b,c d]
      I would be interested 
      1. to know the properties of this coupled system. For example, what is the response 
time of x and y to perturbations in any of the 4 parameters of the system (or combination 
of them along eigenvectors or not), the relaxation time to steady-state of the bulk system? 
      2. How can I plot with MathLab the dynamic response to any kind of time-dependent 
perturbations in one of the parameter (basic step function, sinusoidal forms etc)?
Note that I have found some reference to ''state space models'' in Mathlab help, but I 
am not sure if that applies to this problem and how to implement it.
   Thank you for your help.