In this work, we have investigated the nonlinear oscillations and chaotic dynamics of perturbed bilayer graphene-like structures. The potential energy surface (PES) of bilayer graphene-like geometries is obtained by considering interactions of a co-aligned and counter-aligned arrangement of atoms. We studied the dynamics using the Poincaré surface of section for co-aligned hydrofluorinated graphene (HFG) and counter-aligned hexagonal boron nitride (h-BN) and generalized it for other systems using various choices of interaction parameters. The nature of the oscillations is understood via power spectra and the Lyapunov exponents. We found that the PES is very sensitive to the perturbation for all bilayer graphene-like systems. It is seen that the bilayer HFG system displays chaotic oscillations for strong perturbation, while for the h-BN system, the signature of chaos is found for weak perturbation. We have also generalized the work for perturbed bilayer graphene-like geometries, considering different interlayer interactions and the strength of perturbation. We found a signature of transition from regular to quasiperiodic and finally chaotic oscillations tuned via the strength of the perturbation for these geometries. The nature of the equilibrium points for bilayer graphene-like systems is analyzed via Jacobian stability conditions. We found three stable nodes for co-aligned HFG and counter-aligned h-BN systems for all interaction strengths. Though all other nodes are unstable saddle nodes, the signature of a local bifurcation is also found for weak perturbation.

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