Hypersonic airbreathing vehicles are characterized by highly-integrated airframe and propulsion system. Computational Fluid Dynamics (CFD) tools have been used extensively in the design and analysis phrase of hypersonic vehicles. In this paper, an engineering method and a finite volume method based on the center of grid are developed for preliminary research of interested integrative hypersonic...

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, incl...

We study a class of planar integrate and fire models called adaptive (AIF) models, which possesses an adaptation variable on top membrane potential, whose subthreshold dynamics is piecewise linear . These AIF therefore have two reset conditions, enable bursting to emerge for suitable parameter values. Such can be thought as hybrid dynamical systems. consider particular slow within prove the exi...

Improvement in terminal accuracy is an important objective for future artillery projectiles. Generally it is often associated with range extension. Various concepts and modifications are proposed to correct the range and drift of artillery projectile like course correction fuze. The course correction fuze concepts could provide an attractive and cost-effective solution for munitions accuracy im...

In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the attracting equilibrium (or of another attrac...

Fast-slow systems are studied usually by “geometrical dissection” [4]. The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics which is seen as a parameter of the fast dynamics. A generic solution comes close to a connected component of the stable invariant sets of the fast dynamics. As the slow dynamics evolves, this attractor may lose its stability an...

Mixed-mode dynamics is a complex type of oscillatory behavior that is characterized by an alternation of small-amplitude oscillations and large-amplitude excursions. In this overview article, we focus on one particular mechanism that has been shown to generate mixed-mode oscillations (MMOs) in multiple-scale systems: the generalized canard mechanism. After a brief review of the classical canard...

We analyze a biophysical model of a neuron from the entorhinal cortex that includes persistent sodium and slow potassium as non-standard currents using reduction of dimension and dynamical systems techniques to determine the mechanisms for the generation of mixed-mode oscillations. We have found that the standard spiking currents (sodium and potassium) play a critical role in the analysis of th...

During the evolution of a design concept, designers must integrate diverse sources and kinds of information about requirements, constraints, and tradeoffs. In doing so, they make certain assumptions and develop criteria against which alternatives are evaluated for suitability. Unfortunately, much of this process is implicit, making later review difficult if not impossible. When requirements cha...