Complex-Periodic Spiral Waves Induced by Linearly Polarized Electric Field in the Excitable Medium

Complex-periodic spiral waves are investigated extensively in the oscillatory medium. In this paper, the linearly polarized electric field (LPEF) is employed to induce complex-periodic spiral waves in the excitable medium with abnormal dispersion. As the amplitude of LPEF is increased beyond a threshold, the simple-periodic spiral wave converts into an irregularly complex-periodic one, in which, the local dynamics exhibit several regular spikes followed by one missed spiking period. Furthermore, with the increase of the LPEF amplitude, the missed spiking period follows different numbers of regular spikes [so-called period-1 (P-1), period-2 (P-2), etc.], even a mix of different periods. Meanwhile, the wavelength of the spiral wave transits from a short to a longer one. The pure-periodic (from P-6 to P-2) spirals generally contain defect lines, across which the phase of local oscillation changes by [Formula: see text]. In contrast, there is no defect line in the mixed-periodic spiral waves. This finding indicates that the defect line is not a necessary feature for complex-periodic spiral waves. Moreover, three types of tip trajectories of pure-periodic spiral waves are identified depending on the periods. That is, the outward-petal meandering, the outward-petal meandering with slow modulation, and drifting tip motion, and the tip trajectories could be used to distinguish them from the complex-oscillatory spiral waves.

On Using a Strong High-Frequency Excitation for Parametric Identification of Nonlinear Systems

This paper describes a new parametric method for the development of nonlinear models with parameters identified from an experimental setting. The approach is based on applying a strong nonresonant high-frequency harmonic excitation to the unknown nonlinear system and monitoring its influence on the slow modulation of the system's response. In particular, it is observed that the high-frequency excitation induces a shift in the slow-modulation frequency and a static bias in the mean of the dynamic response. Such changes can be directly related to the amplitude and frequency of the strong excitation offering a unique methodology to identify the unknown nonlinear parameters. The proposed technique is implemented to identify the nonlinear restoring-force coefficients of three experimental systems. Results demonstrate that this technique is capable of identifying the nonlinear parameters with relatively good accuracy.

Modeling resonant trojan motions in planetary systems

We consider the dynamics of a small trojan companion of a hypothetical giant exoplanet under the secular perturbations of additional planets. By a suitable choice of action-angle variables, the problem is amenable to the study of the slow modulation, induced by secular perturbations, to the dynamics of an otherwise called ‘basic’ Hamiltonian model of two degrees of freedom (planar case). We present this Hamiltonian decomposition, which implies that the slow chaotic diffusion at resonances is best described by the paradigm of modulational diffusion.

Sensitivity to temporal modulation rate and spectral bandwidth in the human auditory system: fMRI evidence

Hierarchical models of auditory processing often posit that optimal stimuli, i.e., those eliciting a maximal neural response, will increase in bandwidth and decrease in modulation rate as one ascends the auditory neuraxis. Here, we tested how bandwidth and modulation rate interact at several loci along the human central auditory pathway using functional MRI in a cardiac-gated, sparse acquisition design. Participants listened passively to both narrowband (NB) and broadband (BB) carriers (1/4- or 4-octave pink noise), which were jittered about a mean sinusoidal amplitude modulation rate of 0, 3, 29, or 57 Hz. The jittering was introduced to minimize stimulus-specific adaptation. The results revealed a clear difference between spectral bandwidth and temporal modulation rate: sensitivity to bandwidth (BB > NB) decreased from subcortical structures to nonprimary auditory cortex, whereas sensitivity to slow modulation rates was largest in nonprimary auditory cortex and largely absent in subcortical structures. Furthermore, there was no parametric interaction between bandwidth and modulation rate. These results challenge simple hierarchical models, in that BB stimuli evoked stronger responses in primary auditory cortex (and subcortical structures) rather than nonprimary cortex. Furthermore, the strong preference for slow modulation rates in nonprimary cortex demonstrates the compelling global sensitivity of auditory cortex to modulation rates that are dominant in the principal signals that we process, e.g., speech.