The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

We report the occurrence of vibrational resonance (VR) for a particle placed in a nonlinear asymmetrical Remoissenet-Peyrard potential substrate whose shape is subjected to deformation. We focus on the possible influence of deformation on the occurrence of vibrational resonance (VR) and show evidence of deformation-induced double resonances. By an approximate method involving direct separation of the timescales, we derive the equation of slow motion and obtain the response amplitude. We validate the theoretical results by numerical simulation. Besides revealing the existence of deformation-induced VR, our results show that the parameters of the deformed potential have a significant effect on the VR and can be employed to either suppress or modulate the resonance peaks, thereby controlling the resonances. By exploring the time series, the phase space structures, and the bifurcation of the attractors in Poincaré section, we demonstrate that there are two distinct dynamical mechanisms that can give rise to deformation-induced resonances, viz: (i) monotonic increase in the size of a periodic orbit; and (ii) bifurcation from a periodic to a quasiperiodic attractor.

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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We investigate the time series of solar wind parameters (interplanetary magnetic field, Bz and solar wind speed, Vx) and geomagnetic indices (disturbance storm time, Dst and auroral electrojet, AE) using wavelet analysis and nonlinear dynamics time series techniques. The data were collected from the Flight Center Space Physics Data Facility (GSFC/SPDF) OMNIWEB interface between 2008 and 2017. Wavelet power spectrum (WPS) analysis assists in breaking down the time series of Bz, Vx, Dst and AE parameters into different scales. It was noted that there is a greater concentration of power between the 512 and 1024 months bands across the Bz, Vx, Dst and AE parameters. We also applied non-linear time series modelling methods to examine the Bz, Vx, Dst and AE parameters. We utilised both the time delay and embedded dimension in computing average mutual information (AMI) and false nearest neighbors (FNN), respectively. The Lyapunov exponent (LE) is used to express the complexity of the nonlinear dynamics based on embedding parameters. The Lyapunov exponents depict positive values which confirm that the complex solar wind parameters and the geomagnetic indices are deterministic chaotic systems. The results show noticeable chaotic characteristics in the Bz, Vx, Dst and AE parameters.