Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays

In this paper, we study the periodic oscillatory behavior of a class of bidirectional associative memory (BAM) networks with finite distributed delays. A set of criteria are proposed for determining global exponential periodicity of the proposed BAM networks, which assume neither differentiability nor monotonicity of the activation function of each neuron. In addition, our criteria are easily checkable. (c) 2005 Elsevier Inc. All rights reserved.

Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Exponential stabilization of neural networks with various activation functions and mixed time-varying delays

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Parameter-dependent H∞ control for time varying delay polytopic systems

This paper addresses the robust stabilization and H_∞ control problem for a class of linear polytopic systems with continuously distributed delays. The control objective is to design a robust H_∞ controller that satisfies some exponential stability constraints on the closed-loop poles. Using improved parameter-dependent Lyapunov Krasovskii functionals, new delay-dependent conditions for the robust H_∞ control are established in terms of linear matrix inequalities.

Existence and global asymptotic stability of positive periodic solution of delayed Cohen-Grossberg neural networks

In this paper, a class of periodic Cohen-Grossberg neural networks with discrete and distributed time-varying delays is considered. By an extension of the Lyapunov-Krasovskii functional method, a novel criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is derived in terms of M-matrix without any restriction on uniform positiveness of the amplification functions. Comparison and illustrative examples are given to illustrate the effectiveness of the obtained results. © 2014 Elsevier Inc. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

New inequality-based approach to passivity analysis of neural networks with interval time-varying delay

This paper is concerned with the problem of passivity analysis of neural networks with an interval time-varying delay. Unlike existing results in the literature, the time-delay considered in this paper is subjected to interval time-varying without any restriction on the rate of change. Based on novel refined Jensen inequalities and by constructing an improved Lyapunov-Krasovskii functional (LKF), which fully utilizes information of the neuron activation functions, new delay-dependent conditions that ensure the passivity of the network are derived in terms of tractable linear matrix inequalities (LMIs) which can be effectively solved by various computational tools. The effectiveness and improvement over existing results of the proposed method in this paper are illustrated through numerical examples.

Probability distributed time delays: integrating spatial effects into temporal models

Background In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive. Results We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation. Conclusions Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.

An Efficient Load Distribution Strategy for a Distributed Linear Network of Processors with Communication Delays

In this paper, we present an improved load distribution strategy, for arbitrarily divisible processing loads, to minimize the processing time in a distributed linear network of communicating processors by an efficient utilization of their front-ends. Closed-form solutions are derived, with the processing load originating at the boundary and at the interior of the network, under some important conditions on the arrangement of processors and links in the network. Asymptotic analysis is carried out to explore the ultimate performance limits of such networks. Two important theorems are stated regarding the optimal load sequence and the optimal load origination point. Comparative study of this new strategy with an earlier strategy is also presented.

Managing interprocessor delays in distributed recursive algorithms

For a class of distributed recursive algorithms, it is shown that a stochastic approximation-like tapering stepsize routine suppresses the effects of interprocessor delays.

On the structure of state-feedback LQG controllers for distributed systems with communication delays

This paper presents explicit solutions for a few distributed LQG problems in which players communicate their states with delays. The resulting control structure is reminiscent of a simple management hierarchy, in which a top level input is modified by newer, more localized information as it gets passed down the chain of command. It is hoped that the controller forms arising through optimization may lend insight into the control strategies of biological and social systems with communication delays. © 2011 IEEE.