property + dynamic response of coupled differential equations

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MATT
MATT am 28 Aug. 2018
Bearbeitet: MATT am 29 Aug. 2018
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.

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