We present a geometric singular perturbation analysis of a chemical oscillator. Although the studied three-dimensional model is rather simple its dynamics are quite complex. In the original scaling the problem has a folded critical manifold which additionally becomes tangent to the fast bers in a region relevant to the dynamics. Thus normal hyperbolicity of the critical manifold is lost in two ...

To study the acquisition of perceptual-motor skills as an instance of dynamic pattern formation, we examined the evolution of postural sway and eye and head movements in relation to changes in performance, while 13 novices practiced 3-ball cascade juggling for 9 weeks. Ball trajectories, postural sway, and eye and head movements were recorded repeatedly. Performance improved exponentially, both...

Hebb's idea of a cell assembly as the fundamental unit of neural information processing has dominated neuroscience like no other theoretical concept within the past 60 years. A range of different physiological phenomena, from precisely synchronized spiking to broadly simultaneous rate increases, has been subsumed under this term. Yet progress in this area is hampered by the lack of statistical ...

Multiple time scale methodologies have gained widespread use in molecular dynamics simulations and are implemented in a variety of ways across numerous packages. However, performance of the algorithms depends upon the details of the implementation. This is particularly important in the way in which the nonbonded interactions are partitioned. In this work, we show why some previous implementatio...

In this research, two joint evaluation rating methods (focus-on-attribute and drag-and-drop) and a separate evaluation rating method (focus-on-stimulus) are proposed for rating multiple visual stimuli with respect to multiple scales. All three interactive methods incorporate a real-time adjusting mechanism, allowing respondents to interactively adjust their ratings. Using the traditional paper-...

A neuron embedded in an intact brain, unlike an isolated neuron, participates in network activity at various spatial resolutions. Such multiple scale spatial dynamics is potentially reflected in multiple time scales of temporal dynamics. We identify such multiple dynamical time scales of the inter-spike interval (ISI) fluctuations of neurons of waking/sleeping rats by means of multiscale analys...

The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be  applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinea...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.