Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales

Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

<General Physics, Plasma Dynamics, and Communication Sciences and Engineering< Quarterly Progress Report No. 77, Period Ending 28 Feb. 1965

Physics, plasma dynamics, and communication sciences and engineerin

QUANTUM HARDWARE OF LIVING MATTER

This book belongs to a series of online books summarizing the recent state Topological Geometrodynamics (TGD) and its applications. TGD can be regarded as a unied theory of fundamental interactions but is not the kind of unied theory as so called GUTs constructed by graduate students at seventies and eighties using detailed recipes for how to reduce everything to group theory