Regular dynamics of active particles in the Van der Pol-Morse chain

The regular dynamics of active particles coupled by the Morse potential with Van der Pol dissipation is studied numerically and analytically. It was found that in the system under study, stable propagation of soliton-like perturbations and two types of kink, slow and fast, is possible. It is established that parameters of slow kink are determined from the Abel equation of the first kind, and the front of fast kink is described by a second-order equation integrable in Jacobi elliptic functions. It is shown that the shape of the leading front of the soliton-like perturbation is described by a reduction of the integrable Tzitzeica equation, while the model of its trailing front is reduced to the first kind Abel equation. In a chain with fixed boundary particles, the mode of stable propagation of a kink with elastic reflection from the chain boundaries is revealed. In a chain with periodic boundary conditions, a new type of attractor is revealed in the form of soliton-like perturbations propagating from generator to absorber. It is found that in chain with random initial conditions, generators and absorbers of soliton-like perturbations appear in pairs, the number of which is proportional to the chain length.

Automated summary

The study on active particles coupled by the Morse potential with Van der Pol dissipation reveals the existence of soliton-like perturbations and two types of kink, slow and fast. The parameters of the kinks are determined by different mathematical equations and the propagation modes of the perturbations in different boundary conditions are investigated.