In this paper introducing novel mathematical approach to reduce the computational effort of non-linear problems and the technique called as novel technique. In this paper solve the Duffing and Duffing-Holmes equations by using novel technique is described clearly. This method consists of decomposing a given differential equation in to linear, non-linear and remainder terms. The method has been ...

Abstract In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in presence process noise. Control-based continuation is used to measure both stable and unstable periodic solutions, while different levels noise are injected into system. Using these data, robustness control-based algorithm its ability capture noise-free system assessed by id...

By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak...

This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator ...

1 abstract We study equilibrium solutions for the problem u t = ε 2 u xx − u 3 + λu + cos x u x (0, t) = u x (1, t) = 0. Using a shooting method we find solutions for all non-zero ε. For small ε we add to the solutions found by previous authors, especially Angennent, Mallet-Paret and Peletier, and by Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new resu...

The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyap...

The dynamics of an electret-based, capacitive, vibration-to-electric micro-converter (energy scavenger) is described by a set of ODEs where a second-order equation is coupled to two first-order equations through strongly-nonlinear terms. The nonlinear regimes of forced oscillations are analyzed with a semi-analytical approach, finding that the system exhibits features typical of Duffing-like no...

We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy–Green strain tensor computed from the flow map of the forced mechanical system. This...