Why can blood vessel contraction be described as a second order system?
Many systems have this property. The plot you are looking at is the plot of the transfer function for blood vessel diameter vs time. A trick in mathematics or engineering is to understand a system is to sometimes look at at different system with the same properties that you do understand. For instance, a mass springer damper system is similar to a RLC circuit. That is, if we understand the mass spring damper system, we view the RLC circuit as the analog to the mechanical system and vice versa. In the case of blood pressure, we also have a driven force (the heart). Thus, an extremely simple model would be
$$
m\ddot{x} + c\dot{x} + kx = F(t)
$$
As we see below, the mass spring damper model produces the a similar plot of the transfer function. If you understand the mechanical system or RLC circuit, you can look at your plot parameters as an analog to one of these systems to understand the dynamics occurring in the body.



A more interesting question is can we use PID control to manage the overshoot, rise time, and settling time of the vessel diameter in the body?



The differential equation that models this process is probably related to a Bernoulli differential equation.


http://en.wikipedia.org/wiki/Bernoulli%27s_principle
page 15 http://www.physics.usyd.edu.au/~jbryant/Fluids/Fluidslect4.pdf
http://bme.ccny.cuny.edu/faculty/bfu/blood%20flow%20permeability%20in%20microvessels.pdf


A precise differential equation will need to account for pressure (Bernoulli), fluids (Navier-Stokes), and the elasticity of the vessel walls.