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Classical motion of complex 2-D non-Hermitian Hamiltonian systems is investigated to identify periodic, unbounded and chaotic trajectories. The caustic curves, the Lyapunov exponents, and spectral analysis have been used to identify periodic and chaotic trajectories. Using classical trajectories, we were able to predict quantum transition frequaencies of pseudo-Hermitian non-𝒫𝒯 symmetric systems accurately. This indicates that there exists a correspondence between classical mechanics and quantum mechanics for certain non-Hermitian Hamiltonians as in the case of real Hermitians.