Two floating camphor particles interacting through lateral capillary force

We consider a mathematical model for a two-particle system driven by the spatial gradient of a concentration field of chemicals with conservative attractive interactions in one dimension. This setup corresponds to an experimental system with floating camphor particles at a water surface. Repulsive interaction is introduced, as well as self-propelling force, through the concentration field of camphor molecules at the water surface. Here we newly adopt the attractive lateral capillary force due to the deformation of the water surface. The particles experience competing dissipative repulsion and conservative attraction. We numerically investigated the mathematical model, and found six different modes of motion. The theoretical approach revealed that some of such mode transitions can be understood in terms of bifurcation.