Riddled basins and noise-induced chaos in coupled optomechanical systems

Abstract We investigate a six-dimensional (6D) dual-oscillator optomechanical system, where two mechanical resonators couple to a single optical mode, and show that noise acts as a control parameter that both accelerates the route to chaos and generates riddled basins —fractal intermingling of synchronized and anti-synchronized attractors. Combining Poincaré sections, 2D/3D phase-space projections, the full Lyapunov spectrum, Kaplan–Yorke dimension, Melnikov analysis, and Fokker–Planck diagnostics, we obtain a quantitative and self-consistent picture of noise-induced complexity. As the laser drive increases, a Feigenbaum-type period-doubling cascade culminates in chaos and hyperchaos ( λ 1 > 0; λ 1 , λ 2 > 0 with D KY ∈ [2, 4] ), while Melnikov predictions confirm homoclinic intersections underlying global instability. Riddled-basin formation is demonstrated and quantified by a stability index σ = 0.3–0.6, (ii) fractal basin dimension D B ≈ 1.2–1.55, and (iii) basin entropy S B ≈ 0.3–0.45, all peaking in the noise-driven regime. Transverse Lyapunov exponents along the synchronized and anti-synchronized attractors remain negative (transverse stability), while transversely unstable periodic orbits embedded in the attractors provide the dynamical mechanism for riddling. A critical noise threshold D c ≈ 0.05 is identified for attractor switching and the smearing of bifurcation structure; largest-exponent maps λ 1 ( E , D ) correlate these transitions with parameter space. Our results establish rigorous evidence for noise-modulated (hyper)chaos in high-dimensional optomechanics and offer predictive levers (detuning, coupling, and noise engineering) for controlling instability in microcavity and LIGO-type platforms, as well as enabling applications in chaos-based photonics and sensing.