Considering the effect of geometric nonlinearity and uniformly distributed time-varying temperature, the bifurcation behaviors and chaotic phenomena of a bimetallic thin circular plate are investigated. First of all, the nonlinear dynamic equation for bimetallic plate is established and further reduced to Duffing equation of harmonic parametric excitation, from which the pitchfork bifurcation p...

A modified explicit hybrid method with four stages is presented, the first stage exactly integrating exp(wx), while remaining integrate sin(wx) and cos(wx). Special attention paid to phase properties of during process parameter selection. Numerical comparisons proposed existing methods for several second-order problems show that gives high accuracy in solving Duffing equation Kramarz’s system.

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...

An information signal can be embedded in a transmitter which produces a chaotic signal, it is inviable to the observer who has no knowledge about the transmitter, but it can be recovered if the receiver is a replica of the chaotic transmitter. In this paper, a new aspect of the chaotic communication is introduced. A highgain observer at the receiver’s end replaces the conventional chaotic syste...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

The stable and unstable manifolds associated with a saddle point in two-dimensional non–areapreserving flows under general time-aperiodic perturbations are examined. An improvement to existing geometric Melnikov theory on the normal displacement of these manifolds is presented. A new theory on the previously neglected tangential displacement is developed. Together, these enable locating the per...

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...