Coexisting orbits and chaotic dynamics of a confined self-propelled particle

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.