Homoclinic orbits in the dynamics of articulated pipes conveying fluid

A model is considered representing an elastically jointed pair of articulated pipes conveying fluid. The motion is described by a four-component system of autonomous ordinary differential equations. Numerical techniques are used to investigate changes in the dynamics as two parameters are varied. These parameters represent the fluid flow-rate and a form of symmetry-breaking. Evidence is found that the global bifurcation picture is surprisingly complicated, involving chaos and two types of homoclinic behaviour: namely, Sil'nikov homoclinic orbits to a saddle-focus stationary point, and homoclinic tangencies to periodic orbits. Local theory respective to each type of homoclinicity is reviewed and compared with the numerical results.