Recently, it has been shown that purely anti-aligning interaction between active particles may induce a finite wavelength instability. The formed patterns display intricate spatiotemporal dynamics, suggesting the presence of chaos. Here, we propose a quasi-one-dimensional simplification of the particle interaction model. This simplified model allows us to deduce amplitude equations that describe the collective motion of the active entities. We show that these equations exhibit chaotic orbits. Furthermore, via direct numerical simulations of the particle's system, we discuss the pertinence of these amplitude equations approach for describing the particle's self-coordinated motions.