Question: help with non linear differential equations

Hi, i am new at this forum, and i was wondering if somebody could help whit a  non linear differential equations system, is it posible to know what kind of system is? (damped, overdamped etc) and the time of response, does exist any method to do that?, the system is this:

dp1/dt =exp-(c + p1 + q1)

dq1/dt=exp-(c+q1+p2)

dq2/dt = exp-(c+q2+p1)

dp2/dt = exp-(c + p2 + q2)

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