The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describes a diverse array of physical systems. It has been shown to be relevant in understanding chaos in the classical to quantum transition. Here we explore the complexity of its dynamics in the classical and semi-classical regimes, using the techn...

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the dual role of noise in regularizing the semiclassical Wigner function and averaging over fine structures in classical phase space. The results are interpreted i...

This paper deals with the dynamics of a model describing systems eonsisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is...

A new type of weak signal detection system that combines the memristor and Van der pol-Duffing chaotic has been proposed in this paper, dynamic characteristics are studied. It is observed can change from a state to periodic under different driving force amplitudes. Moreover, numerical simulation results show accuracy up $$1\times 10^{-9}$$ , detectable signal-to-noise ratio reaches -163dB. Comp...

We investigate the conditions under which an optimal continuous feedback control can be achieved. Chaotic oscillations in the single-well Duffing model, with either a positive or a negative nonlinear stiffness term, are tuned to their related Ritz approximation. The Floquet theory enables the stability analysis of the control. Critical values of the feedback control coefficient fulfilling the o...

BACKGROUND Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes relat...

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...

Conventional control systems often suffer from the coexistence of nonlinearity and uncertainty. This paper proposes a novel brain emotional neural network to support addressing such challenges. The proposed integrates wavelet into conventional learning network. is further enhanced by introduction recurrent structure employ two networks as channels therefore combines advantages function, mechani...

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on Melnikov method, necessary critical conditions for in system obtained, chaos threshold curve is obtained by calculation numerical simulation. The accuracy analytical result proved some typical simulation results, including local d...