Vol. 3, No. 1 (2014): Regular Issue

A new approach to path tracking design based on fractional prefilter was developed in this paper. In path tracking design, the dynamic of actuators must be taken into account in order to reduce over- shoots appearing for small displacements. Taking into consideration the maximum velocity, acceleration, jerk, and the bandwidth of the closed-loop on which the input is applied, it permits the generation of an optimal movement reference-input giving a minimum path comple- tion time. An approach to path tracking based on fractional prefilter has been developed. This approach based on a Davidson-Cole (DC) and Frequency Band Limited Fractional Differentiator (FBLFD) pre- filters, with position input. This work describes an extension of this method. It consists of a path tracking using fractional differentiation and comparison between different types of prefilters by direct opti- mization of an Input/Output (I/O) transfer function with speed and acceleration inputs. Fractional differentiation has been used through a Davidson-Cole and frequency band-limited fractional differentiator (FBLFD) prefilters. A simulation on a motor model validates the developed methodology.

A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The mathematical conditions associated with bimodality have been established. The critical factors necessary for both a breaking of symmetry and a transition from bimodal to uni-modal behaviour, in the manner of a bifurcation, have been analysed.

A generalization of S. Lie’s classification of second order ODEs on two-dimensional algebras of point symmetries is constructed. First integrals for found types second order ODEs are reduced. The pos- sibility of the determination of two-dimensional algebras of dynamic symmetries over number field is considered. Interconnection of dy- namic and contact symmetries is demonstrated. On a concrete ex- ample it is shown the procedure of the decomposition of a contact transformation into superposition of point transformation and Leg- endre transformation.

We study the dynamical behavior of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an essentially nonlinear attachment and compare the behavior of the initial system to the Slow Invariant Manifold (SIM). The dynamics of the slow flow can be simple, making regular oscillations in the region of the stable branches of the SIM, having relaxation oscillations or chaotic behavior.The initial system oscillates in the region of the SIM, verifying that the SIM plays an essential role for the dynamics of the initial system.

We present an analysis of phase dynamics of two coupled limit cycle oscillators where coupling is provided by a simple surface acoustic wave (SAW) delay line and the coupled oscillators are either SAW delayed or direct self-feedback type. Synchronization and stability analyses are carried out with primary motivation to explore whether coupling SAW device in synchronization mode could make better sensing platform compared to usual SAW feedback oscillator. Also, the parametric dependencies of the phase dynamics are analyzed to determine whether SAW-coupled oscillators could become stable chaotic code generators for secure communication. Both limit cycle and chaotic dynamics are seen to occur in different regions of parametric space. It is found that by proper tuning of system parameters sensitivity can be enhanced by several orders of magnitude resulting in possibility for making advanced SAW sensor system.

A mathematical model for the dynamics of co-infection of HIV/AIDS and tuberculosis is developed. The model includes treatment for both HIV and tuberculosis and vertical transmission for HIV/AIDS. The disease-free equilibrium of the model is computed and its local stabil- ity is proved. The reproduction numbers of the full model and of its two submodels, the HIV only model and the TB only model, are also calculated. Numerical simulations show the disease-free equilibrium. Future work will focus on computing the stability of the endemic equilibria.

The governing differential equation for the free vibration of a rod undergoing finite strain is obtained by means of Hamilton’s principle. The equation contains quadratic as well as cubic nonlinear terms. For the low-frequency analysis of rods, the two harmonics solution is considered for the equation. The Galerkin method is employed to convert the partial differential equation to a system of two nonlinear ordinary differential equations. These equations are solved utilizing generalized differential quadrature(GDQ) and continuation methods to obtain the backbone curves and also mode shapes of vibration for rods with two different kinds of boundary conditions.

We study soliton solutions for a modified KdV6 equation, modified Boussinesq equation, and KdV equation in (1+1), (2+1) and (3+1) dimensions respectively. Three distinct new dependent variable trans- formations are combined with the simplified form of Hirota’s direct method is used to achieve these soliton solutions. One soliton solution is formally established for each equation together with its associated dispersion relation and dispersion variable.