The definition and description of the dynamics of predator-prey system consists in one of the
fundamental problems of the population biology. Since 1925, several models have been introduced.
Although they are highly effective, most of them neglect certain relevant criteria such as the spatial
and temporal distribution of the studied species. It is with the aim of introducing these criteria that
we conduct our study by coupling two models designed intitially for collective dynamics. The first
is for predators mobility, a Vicsek type model ; The second is a Brownian Particle (BP) model for
prey. We observed, as naturally in the classical models, periodic cycles of the density of predators
and prey. In this case, the period of oscillations depends relatively on the collective dynamics
parameters.

It is well known that all subvarieties of the variety of all semigroups are not absolutely closed. So, it is worth to find subvarieties of the variety of all semigroups that are closed in itself or closed in the containing varieties of semigroups. We have gone through this open problem and able to determine that the varieties of right [left] normal bands and left [right] quasinormal bands are closed in the varieties of semigroups defined by the identities axy = xa^ny [axy = ay^nx], axy = x^nay [axy =ayx^n] (n > 1); and axy = ax^nay [axy = ayx^ny] (n > 1), axy = a^nxa^ry [axy = ay^rxy^n] (n, r ∈ N), respectively.

The goal of this paper is to establish some results for the polar derivative of
a polynomial in the plane that are inspired by a classical result of Turan that relates the
sup-norm of the derivative on the unit circle to that of the polynomial itself under some
conditions. The obtained results sharpen as well as generalize some known estimates that
relate the sup-norm of the polar derivative and the polynomial. Moreover, some concrete
numerical examples are presented, showing that in some situations, the bounds obtained by
our results can be considerably sharper than the previous ones known in very rich literature
on this subject.

In this work, we study the Cauchy problem of the 3d-Anisotropic Boussinesq system with Horizontal dissipation and stratification effect for axisymmetric data. This system couples the Navier-stokes equation with a non-homogenous transport-diffusion equation. More precisely, we prove that this kind of system admits a unique global solution belongs to the Anisotropic Sobolev spaces.

Buy low sell high is one of the basic rules of thumb used by individuals for investment although it
is not considered to be a constructive strategy. In this paper, we show how the appropriate
representation of a minute-by-minute trading time series through ordinal (i.e. permutation) patterns
and the use of a simple decision heuristic may surprisingly result in significant benefits. Using the
proposed approach, we run two experiments. The results provide empirical support for the possible
benefit of using simple decision models, even in the context of chaotic minute-by-minute trading. We don't compare our proposed approach to sophisticated methods in trading, but show how a mathematical model adhering to the idea of bounded rationality may result in significant benefits.

In the present paper, we investigate the order of meromorphic solutions of the homogeneous linear differential-difference equations of the form:

A_n(z)f⁽ⁿ⁾(z+c_n)+...+A₁(z)f^'(z+c₁)+A₀(z)f(z+c₀)=0,

where c₀, ..., c_n are distinct complex numbers and A₀(z), ..., A_n(z) are entire functions having the same order. Under some conditions on the coefficients, we improve and extend some results of Lan and Chen.

The differential entropy of a continuous waveform is defined over the time period spanned by the recording. The time-dependent information dynamics of the observed process are not accessible to this measure. We review here the construction and validation of approximate time-dependent measures of information dynamics.

Local entropy rate (Lizier, et al. Physical Review E, 77, 026110) at time t quantifies information generation at that time. A complementary measure, specific entropy rate (Darmon, Entropy, 18, 190), is the statistical uncertainty in an as yet unobserved future at time t. Specific entropy rate has been used to construct specific transfer entropy (Darmon and Rapp, Physical Review E, 96, 022121) which gives a time-dependent measure of information movement in multichannel dynamical systems. Specific transfer entropy can then be used in a network analysis which results in an asymmetric time-dependent adjacency matrix. Hierarchical transition chronometries in the network can be identified by examining measures derived from the adjacency matrix with quadrant scans of recurrence diagrams (Rapp, et al. NOLTA Conference, 2012).

In this paper, we use the concept of measure of nocompactness and fixed point theorems to investigate the existence and stability of solutions of a class of Hadamard-Stieltjes fractional differential inclusion in an appropriate Banach space, these results are proven under sufficient hypotheses. We also give an example to illustrate the obtained results.

In this paper, different types of nonlinear delay differential equations are solved using the hybrid technique of the differential transform and the Bell polynomial. The obtained results are compared to those obtained previously. The nonlinear terms involved in delay differential equations are handled efficiently with the help of Bell polynomials. The presented technique has been tested on four concrete problems. Different types of errors, such as absolute and maximal, are computed to show the effectiveness and reliability of the method.

This article aims to create commutative hyperstructures, starting with a non-commutative group. So, we consider the starting group to be the dihedral group Dn, with n a natural number, n>1, and we determine the HX groups associated with the dihedral group. For a fixed number n, let Gn be the set of all HX groups. In this paper, we analyze this new structure's properties and find a connection between the divisors of n and the cardinality of Gn. Moreover, this new structure is commutative.