Differential and integral calculus on time scales allows to develop a theory of dynamic equations in order to unify and extend the usual differential equations and difference equations. For single variable differential and integral calculus on time scales, we refer the reader to the textbooks [4, 5] and the references given therein. Multivariable calculus on time scales was developed by the aut...

This paper works on the concept of flatness and its practical application for the design of an optimal transient controller in a synchronous machine. The feedback linearization scheme of interest requires the generation of a flat output from which the feedback control law can easily be designed. Thus the computation of the flat output for reduced order model of the synchronous machine with simp...

Dynamic systems have found their use in sound synthesis as well score synthesis. These levels can be integrated monolithic autonomous a novel approach to algorithmic composition that shares certain aesthetic motivations with some work music systems, such the search for emergence. We discuss various strategies achieving variation on multiple time-scales by using slow-fast, hybrid dynamic and sta...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

We present a novel formulation, called the WaMPDE, for solving systems with forced autonomous components. An important feature of the WaMPDE is its ability to capture frequency modulation (FM) in a natural and compact manner. This is made possible by a key new concept: that of warped time, related to normal time through separate time scales. Using warped time, we obtain a completely general for...

Arguments regarding the appropriate form for the rate at which consumers extract biomass from resource populations hinge on relative time scales of underlying processes. Some ecologists argue that, because differential equation models imply instantaneous rates of change, time scale arguments do not hold. Here we point out that this reasoning is fallacious. We define three natural time scales fo...