Vol. 4, No. 2 (2015): Regular Issue

This paper highlights the interaction between two gaussian pulses propagating inside a dual core optical fiber by the mean of collective variables (CVs) approach. The main result is that energies of the signals being propagated in such fiber with linear coupling always end up being compensated whatever their amplitudes at the entry. It also appears convergence or divergence of the temporal positions of the neighboring solitary waves.

This paper considers unknown input functional fractional order observer design for fractional-order linear time-invariant (LTI) systems with a constant time delay. After given the existence conditions of such observer, based on the fractional order Lyapunov stability approach, a sufficient condition for the asymptotic stability of the estimation error is given in a linear matrix inequality (LMI) formulation. The obtained results are illustrated by a numerical example.

Evolutionary dynamics combines game theory and nonlinear dynamics to model competition in biological and social situations. The replicator equation is a standard paradigm in evolutionary dynamics. The growth rate of each strategy is its excess fitness: the deviation of its fitness from the average. The game-theoretic aspect of the model lies in the choice of fitness function, which is determined by a payoff matrix. Previous work by Ruelas and Rand investigated the Rock- Paper-Scissors replicator dynamics problem with periodic forcing of the payoff coefficients. This work extends the previous to consider the case of quasiperiodic forcing. This model may find applications in biological or social systems where competition is affected by cyclical processes on different scales, such as days/years or weeks/years. We study the quasiperiodically forced Rock-Paper-Scissors problem using numerical simulation, and Floquet theory and harmonic balance. We investigate the linear stability of the interior equilibrium point; we find that the region of stability in frequency space has fractal boundary.

In the present study, we consider the steady two-dimensional stagnation point flow due to a stretching surface in an ambient fluid. The fluid is viscous, incompressible and electrically conducting near the stagnation region on a stretching surface. A uniform magnetic field of strength B is applied in the positive y.direction normal to the stretching surface. The equations governing the flow are solved using Homotopy Analysis Method (HAM). The flow variables are computed in the form of a series with its coefficients containing the parameters such as the magnetic field and the ratio of stretching velocity so that the effect of these parameters on the flow variables can be computed without much computational effort. The optimal values of the convergence control parameters and the the averaged squared residual errors are computed for the flow variables. The software Mathematica is used to perform all the semi-analytical calculations. It was observed that the effect of ratio of stretching velocity V0 on flow velocity is very significant in the sense that zero skin friction occurs at V0 = 0.5. and the trend in the variation of velocity profiles as well as skin friction coefficients are just opposite for V0 < 0.5 and V0 > 0.5.

Polygon-shaped longitudinal large-scale waves are described by means of higher-order shallow water approximation corresponding to the Cauchy–Poisson free boundary problem on the stationary motion of a perfect incompressible fluid circulating around a circle. It is shown that there are four basic physical parameters, which exert an influence on a wave number (or wave length), which is one of the basic values used to characterize the planetary flow pattern in mid-troposphere. Some analogy with the jet-stream following hexagon-shaped path at Saturn’s north pole is observed.

A study of a variable-coefficient Gardner equation is carried out. The subclasses of the equation which are nonlinear self-adjoint have been determined. Conservation laws have also been obtained using two different methods: the direct method of the multipliers and Ibragimov’s theorem based on nonlinear self-adjointness of the equation. It has shown that for this equation conservation laws obtained by using both methods are equivalent.

This paper presents a mathematical strategy for exploring the dynamical behavior of bio-chemical model in temporal morphogenesis which is a generalization of the model studied by Gierer-Meinhardt. We here study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are also carried out.

Foreign Object Debris (FOD) is debris or article alien, which may have fallen onto a runway or taxiway, would potentially cause damage to aircraft. FOD surveillance system is used to FOD surveillance system as a significant technology. However, FOD is a kind of relatively random and diverse target that makes it difficult to analyze and recognize. In the reality, the primary goal of FOD recognition cannot recognize FOD accurately, because airport staffs do not care much about what exactly the FOD is but how great the FOD could threat to airplane. Therefore, based on FOD image features definition and threat level model, we proposed a simple and efficient method to estimate the FOD threat level. By comparison with BP neural network model, the error of new FOD threats coefficient model are no more than 15%. There are five sections discussed in the paper. First, the FOD surveillance system was introduced briefly. Second, the features of FOD including color, texture and shape and related extraction algorithm had been discussed. The HSV color model, texture model and normal shape feature like area, perimeter and eccentricity which are all used to describe FOD targets. Fourteen typical FOD targets such as stone fragment, metal chip, piece of rubber, pieces of paper, plastic and small plant are selected as experiment objects. Thirdly, a new FOD threat coefficient model was proposed, in terms of the values of features based on the huge amount of experiment results and human subjective judgment. Next, the threat level classifier was constructed by the BP neural network. The classifier was trained by some experiment FOD targets with given threat level. The others FOD targets were tested. Finally, the recognition and estimation results indicated that the proposed threat level model were effective and efficient, satisfied the robustness and real-time requirement.