Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

Nonlinear dynamics of the magnetic vortex state in a circular nanodisk was studied under a perpendicular alternating magnetic field that excites the radial modes of the magnetic resonance. Here, we show that as the oscillating frequency is swept down from a frequency higher than the eigenfrequency, the amplitude of the radial mode is almost doubled to the amplitude at the fixed resonance freque...

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, v...

We carry out a quantum analysis of a dc superconducting quantum interference device SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear current-dependent inductance, inducing an external flux tunable nonlinear Duffing self-interaction term in th...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

In this paper, an extensive analysis of a stochastically excited one-degree-of-freedom mechanical system with cubic nonlinearity is presented. This motivated by the need for realistic bifurcation analyses stochastic dynamical systems, given that many physical applications contain significant time-varying uncertainty can lead to drastically different solutions from deterministic case. The propos...

We consider the discrete gradient method for dissipative linear-gradient systems, which strictly replicates the dissipation property, yielding a remarkable stability. However, it also replicates the nonlinearity of an original equation. To overcome this, we can employ multistep linearly implicit schemes as a relaxation; however, it can in turn destroy the originally aimed stability. Matsuo–Furi...

Chaotic motions of a Rayleigh-Duffing oscillator with periodically external and parametric excitations are investigated rigorously. Chaos arising from intersections of homoclinic orbits is analyzed with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters is discussed. Chaotic dynamics are also compare...