Vol. 3, No. 2 (2014): Regular Issue

Recently the dynamics of group chase-and-escape has attracted many physicists. We highlight the biological behaviors and the underlying mathematical rules and physical laws involved in the dynamics of chase-and-escape during the process of hunting in groups. We discuss some recently proposed stochastic models for such a system which revealed various universal statistical features and show how slight variation of the behavioral rules or the interaction parameters can lead to very different statistical behaviors. A number of possible challenging questions are addressed that might led to develop a more life-like model for this novel enthralling dynamical problem.

In this work we establish new one-dimensional discrete dynamical systems: a family of unimodal maps that is proportional to the right hand side of Richards’ growth equation. We investigate in detail the bifurcation structure of Richards’ functions, on the twodimensional parameter space (β,r), where β is the shape parameter, related with the growth-retardation phenomena, and r is the intrinsic growth rate. Sufficient conditions are provided for the occurrence of extinction, stability, period doubling, chaos and non admissibility of Richards’ dynamics. We consider networks having in each node a Richards’ function. We prove some results about the synchronization level when fixing the network topology and changing the local dynamics expressed by the Lyapunov exponents, which depends on the (β,r) parameters. Moreover, we fix the local dynamics and prove results about the synchronization when the network topology change for some kind of networks. Finally, using numerical simulations, we compute the Lyapunov exponents to measure the system complexity, we obtain synchronization intervals of these networks, and we discuss the evolution of the synchronization level in terms of the parameters Richard’s function.

The interest in the use of Raman spectroscopy in cancer diagnosis is due to its capability to unveil the evolution of the biochemical composition of tissue and cells throughout disease progression. Differences between Raman spectra of normal and malignant tissues and cells, both in vivo and in vitro, are being used as a method for the early detection of cancer. In this survey paper we review recently published works related to the analysis of data resulting from Raman spectroscopy. We structure our analysis according with the three steps of the process: data preprocessing, data reduction and data classification.

We are interested in investigating the applicability of the Operational Tau method to solve optimal control problems. The present work focuses on quadratic regulator problems defined on infinite time. For the numerical approximation of the solution, domain transformation technique is studied as well as a special treatment of orthogonal polynomial basis. Numerical resultsobtained via a MATLAB implementation of the proposed approach are shown, illustrating its effectiveness.

Apparently random financial fluctuations often exhibit complexity, chaos. Predictability of limited length time series is hard to infer. Knowledge about the process driving the dynamics facilitates such analysis. This paper shows that quarterly inventory changes of wheat in the global market, during 1974-2012, follow a nonlinear deterministic process. Weakly chaotic behavior alternates with non-chaotic behavior. Cubic dependence of price changes on inventory changes leads to establishment of Duffing Oscillator model as suitable for examining the inventory changes. Endowing parameters with suitable meanings, one may infer temporary speculation changes reflect inventory volatility that drives the transitions between chaotic and non-chaotic behaviors.

This paper concerns with solutionof a Generalized Diffusion-Wave Equation (GDWE) defined in a bounded space domain. In the model proposed, the GDWE is defined using operator BαP introduced recently. In contrast to fractional derivatives which employ fractional power kernels in their definitions, operator BαP allows the kernels to be arbitrary. Therefore, it offers more generality to a diffusion-wave equation than a fractional derivativedoes. Intheschemeproposed, the method of separation of variables is used to separate the space and time domains. The space equation in conjunction with boundary conditions are used to identify the eigenfunctions. The time dependent equation is solved analytically for a specific kernel. For a general kernel, a closed form solution for time equation may not be available. For this reason, we present a numerical scheme to solve this equation. The analytical solution for an exponential kernel is used to verify the numerical scheme. Two examples are presented to show applications of these models. It is hoped that operator BαP will allow us to model diffusion-wave behaviors of a system for which fractional derivatives may not be suitable, and the analytical and numerical schemes will allow us to solve these equations.

The goal of this paper is to present a method that can be used to synchronize unified chaotic systems. The method is mainly based on the technology of feedback Linearization of nonlinear control systems. Numerical simulations are then provided to show the effectiveness and feasibility of the proposed chaos control and synchronization schemes.

The paper is aimed at experimentally showing the possibility of energy production by water waves using a new mean of production of green energy which has been proposed recently. Rotations of a floating pendulum, constrained to move vertically, are studied experimentally in the wave flume of the Laboratory of Hydraulics of the Polytechnic University of Marche. After checking the robustness of the rotation for different values of the wave frequency and amplitude, a generator applied to the pendulum pivot is switched on, and it is shown that it is able to produce electric energy. This represents the experimental proof of the feasibility of the underlying idea. The extracted energy is still small, and further developments are required to optimize the system, likely involving control for rotation activation and sustain in irregular waves, but the goal of showing that it is possible to produce energy from sea waves by a pendulum is reached, and the way for new development is opened.