  Valveless pumping assists in fluid transport in various organisms and
engineering systems. In a previous work, to study the actuator impact effects
on valveless pumping, we constructed a piecewise-linear lumped-parameter model
for a closed-loop system, which consists of two distensible fluid reservoirs
connected by two rigid tubes. The preliminary asymptotic and numerical results
of that work indicated that the system dynamics is rather rich and complex, and
strongly depends upon the driving frequency of the actuator (which periodically
compresses one of the distensible reservoirs) and other system parameters.
Here, a more comprehensive numerical study on the aforementioned model is
carried out, so as to clarify how many different types of system responses can
be excited, and to locate the parameter boundaries within which each type
exists. Moreover, by examining the driving-frequency dependences of a number of
characteristic phases (such as the phase of the compression cycle at which the
actuator collides with or separates from the distensible reservoir it acts
upon), the interrelations between different types of system responses are
identified.
