Vol. 2, No. 2 (2013): Regular Issue

A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited for signals having chaotic variations and sporadically regular linear patterns, possibly impaired by noise. We use time-frequency techniques and the Fractional Fourier transform in order to make it robust and easily implementable. The method is illustrated with an example of application: the analysis of chaotic trajectories of advected passive particles. The signal has a chaotic behavior and encounters Lévy flights (straight lines). The method allows to detect and quantify these ballistic transport regions, even in noisy situations.

For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the universe is considered. Moreover, on the basis of specific ansatz proposed in this paper for the cosmological term, the class of exact solutions of the model equations is obtained. Examples for some given laws of the cosmological term evolution are provided. Besides, a formula for the effective equation of state is derived, and the deceleration parameter of the obtained models is studied.

Here are considered in terms of multivariate fuzzy high approximation to the multivariate unit sequences of multivariate fuzzy quasiinterpolation neural network operators. These operators are multivariate fuzzy analogs of earlier considered multivariate real ones. The derived results generalize earlier real ones into the fuzzy setting. Here the high degree multivariate fuzzy pointwise and uniform convergence with rates to the multivariate fuzzy unit operator are given through multivariate fuzzy inequalities involving the multivariate fuzzy moduli of continuity of the N th order (N ≥ 1) H-fuzzy partial derivatives, of the involved multivariate fuzzy number valued function.

Physically significant question on calculation of conservation laws of the Thomas equation is investigated. It is demonstrated that the Thomas equation is nonlinearly self-adjoint. Using this property and applying the theorem on nonlocal conservation laws the infinite set of conservation laws corresponding to the symmetries of the Thomas equation is computed. It is shown that the Noether theorem provides only one of these conservation laws.

We establish the existence and uniqueness of standing solitary wavelike solutions in H2 for certain systems of nonlocal nonlinear equations. These problems involve second order differential operatorswithout Fredholm property.

In this paper, parameter characteristics of the projective synchronization for two gyroscopes with different dynamical behaviors are investigated. The projective synchronization conditions are presented from the theory of discontinuous dynamical systems. From such synchronization conditions, the parameter characteristics for partial and full projective synchronizations for two gyroscope systems are studied. The full projective synchronization can be achieved exactly in finite time instead of asymptotic synchronization in the traditional projective synchronization. The scaling factors in such synchronization are observed through numerical simulations.

In this paper, we have investigated Complete Synchronization, Anti- Synchronization and all possible cases of Hybrid Synchronization of two restricted planar isosceles three-body-problem evolving from different initial conditions using Active Control Technique. Further, the possible role of control functions in the control of Chaos is analyzed. Finally, numerical simulations are performed to illustrate the effectiveness of the proposed control techniques.