The response of a bistable system driven by a rapidly varying time periodic field or noise, to a low frequency weak pumping field at its subharmonic is examined. We show that sustained oscillation at the subharmonic frequency of the weak field can be generated for an optimal strength of rapidly varying field or noise that takes care of detuning arising out of amplitude dependence of frequency due to nonlinearity of the system and when the strength of the pumping field is set above a critical threshold. Our theoretical analysis is corroborated by detailed numerical simulations.

We have analyzed the differential flow-induced instability in the presence of diffusive transport in a reaction-diffusion system following activator-inhibitor kinetics. The conspicuous interaction of differential flow and differential diffusivity that leads to pattern selection during transition of the traveling waves from stripes to rotating spots propagating in hexagonal arrays subsequent to wave splitting has been explored on the basis of a few-mode Galerkin scheme.

We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

The homogeneous stable state of a one-component reaction–diffusion system with positive diffusivity always remains stable by diffusion. We have shown that dichotomously fluctuating diffusivity leads to an instability of the stable state for an optimal range of correlation times of dichotomous noise. The instability condition corresponds to the rare event of instantaneous diffusivity remaining negative for typical realizations of dichotomous fluctuations over a finite correlation time. Detailed numerical simulations reveal that, depending on the characteristic non-linearity of the reaction term, this fluctuating diffusivity-driven instability results in irregular non-stationary patterns in the form of spatio-temporal chaos or phase-separation.

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