Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe

Dynamics of Discrete And Continuous Spatially Distributed Systems

In this dissertation we consider some dynamical systems and their properties. We study the stability of a discrete system, which corresponds to an approximate dynamic programming problem. We investigate phase transition of a process on random graphs and find critical parameters. We analyze the bifurcation and attractor of a system given by generalized Lotka-Volterra equations. In particular:we study the stability of a discrete dynamical system of estimation error, which corresponds to an approximate dynamic programming (ADP) problem via Lyapunov\u27s second method. We prove that the system is uniformly ultimately bounded;we show the necessary conditions for a phase transition in two randomly coupled probabilistic cellular automata in mean-field approximation and prove the existence of limit cycle behavior;we introduce a new random graph model G_{Z^2_N, p_d}, a discrete torus with random edges defined with respect to graph distances between vertices on the torus. We prove that the degree probability distribution is approximately Poisson and the diameter of the graph is D(G{Z^2_N, p_d}) = Theta (log N), whp;we study bootstrap percolation on G_{Z^2_N, p_d}. Sharp conditions are derived for phase transition at different values of k with a k-threshold rule in mean-field approximation. We generalize the bootstrap percolation on G_{Z^2_N, p_d} to the case of two types of vertices with a modified k-threshold rule. We derive some bounds for critical probabilities in the generalized model in mean-field approximation;we study the bifurcation of two coupled systems each described by generalized Lotka-Volterra equations with respect to coupling. Also, we study a dissipative system with an inhomogeneous heteroclinic cycle, that is, each equilibrium in the cycle is either with one or two unstable directions. We prove that there exists an asymptotically stable set consisting of unstable manifolds of the saddles. Most of the results in the dissertation has been published, which represent joint work with Svante Janson, Robert Kozma, Mikhail I. Rabinovich, Miklos Ruszinko, Ludmilla D. Werbos, and Paul Werbos

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

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

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