Dynamics of deterministic chaos evolution from vector dissipative solitons under linear coupling perturbation

• Continuous PC tuning reshapes polarization attractors in vector soliton lasers. • Weak linear coupling drives transitions from order to deterministic chaos. • Quasi-periodic vector breathing bridges ordered and chaotic states. The nonlinear dynamical evolution of vector dissipative solitons (VSs) in a passively mode-locked fiber laser provides a rich platform for investigating multi-degree-of-freedom complex systems. In this paper, we numerically investigate the topological transition and deterministic chaotic dynamics of VSs driven by subtle linear coupling perturbations using the coupled Ginzburg-Landau equations. By systematically fine-tuning the polarization control parameters, we reveal a distinct dynamical degradation route: from a stable polarization-locked state to a quasi-periodic vector breathing state, and ultimately into complex polarization chaos. Results demonstrate that as linear coupling constraints are progressively relaxed, the system undergoes bounded periodic phase slippage and the excitation of incommensurate subharmonics, leading to the chaotic deconstruction of the original fixed-point attractor. The deterministic chaotic nature of this state is quantitatively confirmed by a fractal correlation dimension of D ≈ 2.51 and a positive maximum Lyapunov exponent of λ = 0.0732 . These findings elucidate the physical essence of attractor reorganization induced by polarization perturbations, providing a crucial theoretical framework and foundational physical mechanisms for future data-driven modeling and neural network-based prediction of complex laser dynamics.