Pseudo-spectra of the dynamical system

Question is about a Pseudo spectra of the dynamic system. What does a following system of two second order equations say in terms of pseudo-spectral analysis? Here is a system where MATLAB notation is used. x(t) and y(t) are functions of time:

diff(x,2) - 2 * a * diff(y,1) + b^2 * x = 2 * q * a^2 * x,

diff(y,2) + 2 * a * diff(x,1) + b^2 * y = 0.

where b > a > 0 and q are constants. q is a small parameter that can introduce instability in the system.

P.S. This is math & physics related question, and I am asking a pseudo-spectra insight to understand how speudo-spectra 'picture' is related to waves I saw long time ago that are, for example, responsible for produsing a linear instability in the dynamical systems. Here is a link to a specific note that analysis above system the way I used in my research related to space, solar and lab plasma phenomena:

https://www.researchgate.net/publication/333811790_The_Physics_of_Instability_Inhomogeneity_Generated_Waves

[Torsten]

Why do you ask this in a MATLAB forum ? I'd try in a maths or physics forum.

[Walter Roberson]

This does not appear to be a question about MATLAB.

[E K]

In this forum there are many spectra and math related questions too, articles, and even blog posts by people working for MATLAB. Even by Dr. Moler, who I believe had a paper about pseudo-spectra long time ago too. My background is in physics, and I asked for help to those who can explain pseudo-spectra picture.