We have analysed the effect of nonlinearity of an activation function on the oscillation of the neural network with asymmetrical cyclic connections by using the averaging method. The oscillation obtained by linear approximation, in which the activation function is approximated by a linear function, is multi-modal although the actual oscillation with numerical simulation is unimodal. When the ac...

Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply various methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the consider...

The mechanism of entrainment to natural oscillations in a class of (bio)mechanical systems described by linear models is investigated. Two new nonlinear control strategies are proposed to achieve global convergence to a prescribed resonance mode of oscillation within a nite time. E ectiveness of the proposed methods for resonance entrainment is demonstrated by examples of computer simulation fo...

We analyze the modulation instability spectrum in a varying dispersion optical fiber as a function of the dispersion oscillation amplitude, and predict a novel sideband splitting into different sub-sidebands for relatively large dispersion oscillations. OCIS codes: (060.4370) Nonlinear optics, fibers; (190.4380) Nonlinear optics, four-wave mixing;

We consider a certain second-order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed. An example is given. c © 2006 Elsevier Science Ltd. All rights reserved. Keywords—Delay differential equations, Second-order, Nonlinear, Oscillation, Impulses.

This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and of...

We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-Q nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally gen...

Intrinsic localized mode (ILM) is spatially localized and temporally periodic oscillation in nonlinear coupled oscillators. We numerically investigate the dynamical stability of ILMs in a microcantilever array, in which ILMs were experimentally observed by M. Sato et al. It is found that the stability change of ILMs is due to the ratio in nonlinear potentials. This phenomenon also occurs in the...

In this paper, we derive new criteria for evaluating the global stability of periodic oscillation for gene networks with small forcing and delay. Our results rely on the Lipschtiz conditions of Hill function, topology of gene networks. In particular, Our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the c...