Vol. 7, No. 4 (2018): Regular Issue

In this paper we introduce and study the notion I-statistical convergence of order α, and I-lacunary statistical convergence of order a with respect to the intuitionistic fuzzy n-normed space and also we investigate their relationship and some inclusion theorems are roved.

Homologous recombination, and the associated notion of sexual reproduction, are ubiquitous in the evolution of biological organisms. However, there is still no clear, generally accepted understanding of why it exists and under what circumstances it is useful. Here, we argue that its utility is strongly linked to specific types of fitness landscape. In particular, landscapes that are quasi-modular (weak additive epistasis) or redundant (negative epistasis), two properties that are also ubiquitous in biological systems. We further argue that recombination and modularity together are responsible for the formation of “building block hierarchies” where, to make compatible the two different types of building block, landscape blocks associated with modular fitness landscapes and uilding Block schemata defined by the recombination distribution, a meta-evolution is necessary, wherein the recombination distribution itself evolves, leading to recombination hotspots at the boundaries of landscape blocks. We finally argue that recombinative dynamics and modular landscapes are necessary conditions for the formation of building block hierarchies and, ultimately, life itself.

All systems - physical, biological, ecological and social - are composed of hierarchies of building blocks - atoms, molecules, cells, tissues, individuals, species etc. - with corresponding interactions, wherein the presence of interactions - attractive and repulsive - affects the relative spatio-temporal distribution of the building blocks. In physical systems, in particular, the structure of the building blocks and the nature of their interactions has been deduced via systematic observations of their positions in space and time. Unfortunately, Complex Adaptive Systems are highly multi-factorial, so that, unlike many physical systems, it is impossible to systematically observe and characterize each and every interaction that exists in such systems. In this paper we discuss a general framework - Complex Inference Networks - wherein interactions, particularly in Complex Adaptive Systems, may be studied and characterized using position data about their building blocks. We compare and contrast physical versus Complex Adaptive Systems and give as an explicit example the identification of disease hosts in the ecology of emerging and neglected diseases, where it has been possible to discover previously unknown ecological interactions from species co-occurrence data.

Deterministic predictor-corrector schemes are used mainly because of their numerical stability which they inherit from implicit counterparts of their corrector schemes. In principle these advantages carry over to the stochastic case. In this paper a complete study for the linear MS-stability of the oneparameter family of weak order 1.0 predictor-corrector Taylor schemes for scalar stochastic differential equations is given. Figures of the MS-stability regions that confirm the theoretical results are shown. It is also shown that mean- square A-stability is recovered if the parameter is increased.

The present paper is devoted to the investigation into the nonlinear dynamics of Twitter. A newmodel of Twitter as a thermodynamic non-equilibrium system is suggested. Dynamic variables of such system are represented by the variations of tweet/retweet number and instantaneous diversity between the densities of population on different levels around the equilibrium values. Regular and chaotic states of networks are described. It is pointed out, that the system is in a condition of an asymptotically stable equilibrium when the intensity values of an external information are small (the number of tweets eventually tends to its equilibrium value). If the intensity values of external information exceed the critical value, then the chaotic oscillations of tweets are to be observed. We have made the calculations of the correlation dimension and embedding dimension for the dynamics of the 10 most popular @ (TOP 100 by data of Twitter Counter). The results show, that all observed time series have clearly defined chaotic dynamical nature.

In this paper, we study the effect of harvesting on the qualitative properties of predator-prey model with modified Leslie-Gower and Holling Type II functional responses. The model is given by a system of two ordinary differential equations with non-selective constants harvesting terms. We investigate the impact of harvesting terms on the boundedness of solutions, on the existence of the attraction set, on the stability of different equilibrium points. A Lyapunov function is used to prove the global stability of the interior equilibrium. We also, discussed the policy of optimal harvest and we got the solution for the interior equilibriumby the Pontryaginmaximum criterion. Finally, our theoretical results are illustrated by a numerical simulations.

Medical image segmentation plays a crucial role in computer aided diagnosis system that have a significant potential for early detection of skin cancer. The aim of segmentation process in this field is to facilitate the characterization and the visualization of the lesion in dermoscopic images. This paper proposes a new method for improving the lesion border detection in dermoscopic images, based on the ant colony optimization algorithm. Our experiments show that the proposed method achieved a significant improvement in image segmentation when compared to the deterministic canny procedure.

In this paper, by taking advantage of the richness of Fomenko’s theory of surgery on (bifurcations of) Liouville tori, we give a complete description of the topology and bifurcations of the invariant level sets of a heavy rigid body around a fixed point corresponding to the Goryachev-Chaplygin case on sokolov terms. In particular, for all values of the parameters of the system, the bifurcation diagrams of the momentum mapping are constructed, bifurcations of the common level sets of the first integrals are described, explicit periodic solutions were determined, the topology of the invariant manifolds and all generic bifurcations are illustrated numerically.

In this paper, we study the approximate controllability of impulsive neutral functional integrodifferential systems with finite delay. The fractional power theory and a-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability of the impulsive integrodifferential equation are formulated and proved. An example is provided to illustrate the theory.

Dynamic model for brushless motor in the rotating frame is studied in this paper, where a periodic disturbance is introduced in the quadrature-axis voltage. The methodology of discrete implicit maps is adopted to investigate the dynamical response of such brushless motor system. Multiple closed semi-analytic bifurcation routes for period-1 motions are found by varying frequency of disturbance of the quadrature-axis voltage. The stability conditions for periodic motions will be given through eigenvalue analysis. From the semi-analytical prediction of period-1 motions, the corresponding frequency-amplitude characteristics are obtained. Finally, the stable and unstable period-1 motions will be presented numerically. With such discrete implicit maps method, the unstable motion of such brushless motor with strong nonlinearity can be obtained. Compared to the method of generalized harmonic balance, the dimension of Jacobian matrix can be dramatically decreased and the numerical error can be avoided without using QR algorithm.