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The phenomenon of vibrational resonance is studied in a nonlinear dissipative two‐fluid plasma model with an asymmetric single‐well and double‐well potentials driven by an amplitude modulated (AM) signal. The external signal consisting of a low‐frequency (ω) component and two high‐frequencies (Ω+ω) and (Ω−ω) components with Ω>>ω. First, the approximate analytical expression for the response amplitude Q at the low frequency ω is obtained by means of direct separation of the slow and fast motions. We verified the theoretical results by numerical simulation using fourth‐order Runge–Kutta method and found it is in good agreement with the theoretical analysis. We show the enhanced response amplitude at the low frequency ω, showing more number of resonance peaks, a non‐decay of the response amplitude and hysteresis, and a jump phenomenon on the response amplitude curve due to the AM signal. In addition, we studied the effect of nonlinear dissipation on the response amplitude curve. By exploring the phase portrait and the bifurcation diagram, we explain the resonance mechanism and account for the other features of the resonance curve.

The paper highlights the effect of different forms of   periodic   piecewise linear forces in the ubiquitous Duffing oscillator equation. The external periodic piecewise linear forces considered are Triangular, Hat, Trapezium, Quadratic and Rectangular. With the aid of some numerical simulation tools such as bifurcation diagram, phase portrait and Poincare´ map, the different routes to chaos and various strange attractors are found to occur due to the applied forces. The effect of an ε-parametric control force in the Duffing system is also analyzed. To characterize the regular and chaotic behaviours of this system, the maximal Lyapunov exponent is employed.

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We consider a harmonically trapped potential system driven by modulated signals with two widely different frequencies ω and Ω, where Ω >> ω. The forms of modulated signals are amplitude modulated (AM) and frequency-modulated (FM) signals. An amplitude-modulated external signal is consisting of a low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω − ω) whereas the frequency modulated signal consisting of the frequency components such as f sinωt cos(g cosΩt) and f sin(g cosΩt) cosωt. Depending upon the values of the parameters in the potential function, an odd number of potential wells of different depths can be generated. We numerically investigate the effect of these modulated signals on vibrational resonance (VR) in single-well, three-well, five-well and seven-well potentials. Different from traditional VR theory in the present paper, the enhancement of VR is made by the amplitudes of the AM and FM signals. We show the enhanced response amplitude (Q) at the low-frequency ω, showing the greater number of resonance peaks and non-decay response amplitude on the response amplitude curve due to the modulated signals in all the potential wells. Furthermore, the response amplitude of the system driven by the AM signal exhibits hysteresis and a jump phenomenon. Such behavior of Q is not observed in the system driven by the FM signal.