Driven-dissipative nonlinear systems can exhibit global phase-space structures that are not captured by local fixed-point analysis alone. Here we study two coupled Kerr cavities and investigate how a global bifurcation that changes the connectivity of strange attractors is reflected in quantum dynamics. We identify distinct features in quantum-trajectory statistics associated with a single connected strange attractor and with two symmetry-related localized attractors. In the connected regime, the perturbative response remains robust against weak external asymmetries, whereas this robustness is lost after the global bifurcation separates phase space into dynamically disconnected regions. Along the symmetric-driving line, this reorganization is accompanied by the onset of exchange-symmetry breaking. Our results establish a concrete connection between semiclassical attractor connectivity and quantum-trajectory behavior, highlighting the role of global phase-space organization in driven-dissipative nonlinear systems.

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• Open quantum systems & decoherence
• Quantum chaos
• Quantum cavities
• Stochastic differential equations