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

Two floating camphor particles interacting through lateral capillary force