Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.

This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations ...

This paper investigates the lock range of injection-locked non-harmonic oscillators using a frequency-domain approach. By representing a non-harmonic oscillator with a set of harmonic oscillators, the intrinsic relation between the lock range of the harmonic oscillators and that of the non-harmonic is obtained. We show that non-harmonic oscillators exhibit a larger lock range as compared with h...

We show how a topological model which describes the stretching and squeezing mechanisms responsible for creating chaotic behavior can be extracted from the neural spike train data. The mechanism we have identified is the same one ("gateau roule," or jelly-roll) which has previously been identified in the Duffing oscillator [Gilmore and McCallum, Phys. Rev. E 51, 935 (1995)] and in a YAG laser [...

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one-dimensional chaotic dynamical systems. Environmental fluctuations-characteristic of all realistic dynamical systems-suppress the development of a fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function, which would otherwise invalidate ...

Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the 'Internet of Things'. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applicati...