Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance

The Neimark-Sacker bifurcation of a forced vibration system is considered in this paper. The series solution to the motion equation is obtained, and the Poincaré map is established. The fixed point of the Poincaré map is guaranteed by the implicit function theorem. The map is transformed into its normal form at the fifth-order resonance case. For some parameter values, there exists the torus T1. Furthermore, the phenomenon of phase locking on the torus T1 is investigated and the parameter condition under which there exists subharmonic motion on the torus T1 is determined.

Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol–Duffing Oscillators

In this paper, we investigate the codimension-two double Hopf bifurcation in delay-coupled van der Pol–Duffing oscillators. By using normal form theory of delay differential equations, the normal form associated with the codimension-two double Hopf bifurcation is calculated. Choosing appropriate values of the coupling strength and the delay can result in nonresonance and weak resonance double Hopf bifurcations. The dynamical classification near these bifurcation points can be explicitly determined by the corresponding normal form. Periodic, quasi-periodic solutions and torus are found near the bifurcation point. The numerical simulations are employed to support the theoretical results.

Transfer of vibrational coherence through incoherent energy transfer process in Förster limit

We study transfer of coherent nuclear oscillations between an excitation energy donor and an acceptor in a simple dimeric electronic system coupled to an unstructured thermodynamic bath and some pronounced vibrational intramolecular mode. Our focus is on the nonlinear optical response of such a system, i.e., we study both excited state energy transfer and the compensation of the so-called ground-state bleach signal. The response function formalism enables us to investigate a heterodimer with monomers coupled strongly to the bath and by a weak resonance coupling to each other (Förster rate limit). Our work is motivated by recent observation of various vibrational signatures in two-dimensional coherent spectra of energy-transferring systems including large structures with a fast energy diffusion. We find that the vibrational coherence can be transferred from donor to acceptor molecules provided the transfer rate is sufficiently fast. The ground-state bleach signal of the acceptor molecules does not show any oscillatory signatures, and oscillations in ground-state bleaching signal of the donor prevail with the amplitude, which is not decreasing with the relaxation rate.