Localization of spatiotemporal chaos in driven dissipative systems with parabolic potential

Dissipative temporal Kerr soliton (DKS) dynamics [1], [2] in passive Kerr resonators are governed by a Lugiato-Lefever equation (LLE) model. When increasing the Kerr nonlinearity, DKSs undergo different types of instabilities, leading to periodic (e.g., breathers) or chaotic behavior (e.g., spatiotemporal chaos). These unstable states can be stabilized by different mechanisms, such as third-order chromatic dispersion [3] or temporal parabolic potentials [4], [5]. The latter can be generated by an intracavity synchronous phase modulator [6]. Here, we show that spatiotemporal chaos can be confined by adding such temporal parabolic potentials in the center, leading to the formation of a chaoticon. We unveil these chaotic states by analyzing the Lyapunov exponent (LE) of their modal components. In the mean-field approximation, the dynamics of the electric field envelope A(τ,t) propagating within the cavity is governed by the modified dimensionless LLE