The oscillation criteria for forced nonlinear fractional difference equation of the form ∆x(t) + f1(t, x(t+ α)) =v(t) + f2(t, x(t+ α)), t ∈ N0, 0 < α ≤ 1, ∆x(t)|t=0 =x0, where ∆α denotes the Riemann-Liouville like discrete fractional difference operator of order α is presented. Mathematics Subject Classification: 26A33, 39A12

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form str...

This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently...

In 1991, the first paper on impulsive partial differential equations [1] was published. For an excellent exposition of this paper and its applications, see [2]. The oscillation theory of impulsive partial differential equations have wide applications in such subjects as control theory, meteorology, biology, medicine, engineering, chemistry and physics. Many results can be found [3-14]. However,...

In this work, an aeroelastic prediction framework is formulated by blending control-oriented techniques that consist of linear fractional transformation representation, identification of nonlinear operators, and stability boundary prediction for both flutter and limit-cycle-oscillation phenomena. The final product is an efficient tool devised to identify, characterize, and predict flutter/limit...

Keywords--Oscil lat ion, Second-order nonlinear dynamic equation, Time scale, Riccati transformation technique, Positive solution. 1. I N T R O D U C T I O N The theory of t ime scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D. thesis [1] in order to unify continuous and discrete analysis. Not only can this theory of so-called "dynamic equations" unif...

Some oscillation criteria are established for the second order nonlinear neutral differential equations of the form ((x(t) + ax(t− τ1)− bx(t+ τ2)) ) ′′ = q(t)x(t− σ1) + p(t)x (t+ σ2), and (x(t) − ax(t− τ1) + bx(t+ τ2) )′′ = q(t)x(t− σ1) + p(t)x (t+ σ2) where α and β are the ratios of odd positive integers with β ≥ 1. Examples are provided to illustrate the main results.

The theory of integral quadratic constraints is used for performance analysis of nonlinear and uncertain systems. Periodic oscillations induced by sinusodal excitation are studied in particular.

This paper is intended to study the oscillatory behaviour of solutions of the higher order nonlinear neutral type functional dynamic equation with oscillating coefficients of the following form: [y(t) + p(t)y (τ(t))] n + m ∑ i=1 qi(t)fi (y (φi(t))) = s(t) where n ≥ 2. We obtain sufficient conditions for oscillatory behaviour of its solutions. Our results complement the oscillation results for n...

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate "surprises" with important socioeconomic and ecological implications. Paleorecords are key for eluci...