Search

This paper investigates the stability in an exponential sense of complex-valued Bidirectional Associative Memory (BAM) neural networks with time delays under the stochastic and impulsive effects. By utilizing the contracting mapping theorem, the existence and uniqueness of the equilibrium point for the proposed complex-valued neural networks are verified. Moreover, based on the Lyapunov - Krasovskii functional construction, matrix inequality techniques and stability theory, some novel time-delayed sufficient conditions are attained in linear matrix inequalities (LMIs) form, which ensure the exponential stability of the trivial solution for the addressed neural networks. Finally, to illustrate the superiority and effects of our theoretical results, two numerical examples with their simulations are provided via MATLAB LMI control toolbox. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) with mixed delays, in which the bounded distributed and unbounded discrete time-varying delays are involved. Then, under the nonsmooth analysis and Lyapunov stability theory, several easily verified algebraic criteria are established to guarantee the global synchronization of FMNNs via a designed fuzzy feedback controller. Moreover, to show the superiority of the theoretical results, several discussions and comparisons with existing work are provided, indicating that derived results in this paper are general and include several existing ones as special cases. Finally, two numerical examples and two applications in psuedorandom number generation and image encryption are presented to show the validity and practicability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of reduced-order extended dissipative filters design for continuous-time singular Markovian jump systems with discrete and distributed delays. By proposing a new integral inequality, a sufficient condition based on linear matrix inequalities (LMIs) is presented to ensure the existence of the extended dissipative filters. Compared with the previous ones, the proposed method can sufficiently exploit the information on discrete and distributed delays. A set of slack matrices instead of fixed ones are introduced in the LMIs to find all solutions of the reduced-order filters, which can enhance the flexibility of the obtained result. Two numerical examples are provided to illustrate the effectiveness and advantages of the proposed filters design condition. [ABSTRACT FROM AUTHOR]

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time synchronization (FTS) of memristor-based recurrent neural networks (MRNNs) combined with inertial items and mixed delays, where both the discrete delays and bounded distributed delays are included. First, MRNNs with inertial items are of second-order state derivatives, thereby differing from the classical first-order MRNNs and bringing difficulties to study the dynamics of such systems. By using the order-reduction method, such kind of second-order MRNNs is transferred into conventional first-order differential systems. Then, under two kinds of designed feedback controllers, several sufficient conditions are derived ensuring the FTS of MRNNs with inertial items and mixed delays. Finally, numerical simulations are provided to show the effectiveness of the results and one application is also presented in pseudorandom number generation. [ABSTRACT FROM AUTHOR]

In this paper, an output feedback controller with logarithmic function is constructed to address the objective of global regulation for a class of feedforward nonlinear systems with time delays. Firstly, discrete delays and distributed delays are allowed in the input and output as well as states of the considered system. Secondly, compared to the conventional research contributions of state feedback regulation, not only the condition that the output signal is needed to design the control strategy become relaxed, but also the information about the discrete delays and distributed delays that need to be known is less. Finally, different from the existing research results, based on the time-varying gain technology and Lyapunov–Razumikhin theorem, the output feedback global regulation controller constructed here is more lucid in structure and more perfect in function. Two examples are presented to demonstrate the effectiveness of global regulation about the proposed approach for the considered system. [ABSTRACT FROM AUTHOR]

A mathematical model for the quantitative analysis of the interaction between cancer cells and cell-mediated immune system with two discrete-time delays, considering the role of antibodies, is studied in this paper. The model is analyzed both analytically and numerically to understand the dynamics of interaction delay and proliferation enhancement effect delay in the eradication of cancer. Hopf bifurcation occurs when one-time delay crosses the critical value in the absence of the other. It is also observed that as we increase any of the delays, it will increase the cancer burden. The analysis shows that a cancer-free state cannot be obtained solely by the killing rate of cytotoxic T-lymphocytes, but humoral response in combination with cell-mediated immune responses plays an important role to eradicate cancer. [ABSTRACT FROM AUTHOR]

The existing results of passivity for neural networks mainly concentrated on first-order derivative of the states, whereas it is also significant to study the passivity with high-order derivative. In this paper, a class of memristor-based inertial neural networks (MINNs) with external inputs and outputs are concerned. First, by choosing appropriate variable transformation, the original networks are rewritten as first-order differential equations. Then a criterion of passivity for the MINNs is presented by nonsmooth analysis and linear matrix inequality (LMI) techniques, which could also result in NP-hard problem since it needs at least exponential-time to solve the passivity condition. Meanwhile, based on the obtained passivity criterion, asymptotic stability criterion is accordingly derived for MINNs. In order to avoid the NP-hard problem, we employ matrix-analysis-techniques with the property that the difference-matrix between the given matrix and the proposed matrix is seminegative definite. Then the time complexity for solving the proposed passivity criterion is reduced to constant-time with respect to the number of LMIs. Robust passivity for MINNs is also studied for bounded uncertain parameters. The MINN widens the application ranges for designing neural networks. Finally, relevant simulation examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control on predator, the prey species still extinct, whereas the predator species is stable at certain values. Several examples are presented to show the feasibility of the main results. [ABSTRACT FROM AUTHOR]

This paper proposes an output feedback control strategy to achieve the global regulation of a class of large-scale feedforward nonlinear systems with discrete and distributed delays. The nonlinear terms are assumed to be bounded by the continuous functions of inputs multiplied by an unknown constant, and the discrete and distributed delays are allowed in the inputs and states. A novel design approach, namely dynamic gain construct method, is given to design the observers and the output feedback controllers. On the basis of the Lyapunov–Razumikhin theory, the global regulation of the closed-loop system is proved. Different from the existing results, a dynamic gain is online updated by the systems outputs and the observers states. Moreover, the time-varying gain with the logarithmic form is first constructed under a unified framework, which is also a valid control algorithm in coping with the uncertainty of the concerned systems. A simulation example is provided to demonstrate the effectiveness of the theoretic results. [ABSTRACT FROM AUTHOR]

In this paper, a new projection neural network with discrete and distributed delays is presented for solving linear variational inequality problems. Some novel sufficient conditions ensuring globally exponential stability are derived by employing matrix measure and differential inequality technique, and the easily checkable conditions are less restrictive. Furthermore, based on the Lagrange multiplier, the proposed neural network can solve the quadratic programming problems. Finally, some simulation results with applications to finance and image fusion are given to demonstrate the effective performance of the neural network. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the stability in a new model of imitation dynamics with discrete distributed delays. Some sufficient conditions of the asymptotical stability for the interior Nash equilibrium of the imitation dynamics with multiple-delay are obtained. Finally, numerical experiments are displayed which support the theoretical results through the Snowdrift game. Highlights • Investigating the stability of the imitation dynamics with discrete distributed delays. • Deriving the sufficient conditions for the imitation dynamics with two delays and multi-delay. • Illustrating the effectiveness of the results through Snowdrift game. [ABSTRACT FROM AUTHOR]

Abstract: Multimedia applications are usually resource intensive, have stringent quality of service requirements, and in many cases involve large groups of participants. Multicasting is poised to play an important role in future deployment of these applications. This paper focuses on developing delay-bounded, minimum-cost multicast trees, linking a source to a set of multicast destination nodes. The approach taken in this paper is efficient, flexible and unique in the sense that it cleverly limits its computation only to paths that originate at multicast nodes, thereby avoiding computing paths that exclusively link non-multicast nodes. The simulation results show that the multicast trees produced by the proposed heuristic are of lower cost than those produced by other well-known heuristics, including those which use an expensive k-shortest-paths procedure to minimize the cost of the multicast tree. Furthermore, the results show that, in comparison to other heuristics, the proposed scheme results in a significant reduction in the computation time required to build the multicast tree. [Copyright &y& Elsevier]

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates, the globally exponential stability analysis problem for a class of markovian jumping Cohen–Grossberg BAM-type neural networks (CGBAMNNs) with mixed time delays and impulsive effects. Here the jumping parameters are considered, which are governed by a markov process with discrete & finite state space. The mixed time delays carries both discrete time-varying and distributed delays, which means the lower and upper bounds of discrete time delays are available. By fabricating an appropriate Lyapunov–Krasovskii functional (LKF), some new sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) to guarantee the globally exponential stability for the labeled neural networks. The obtained conditions are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. Furthermore, we have collated our effort with foregoing one in the available literatures and showed that it is less conserved. Finally, three numerical examples with their simulative reactions are provided to demonstrate the viability of the notional outcomes. [ABSTRACT FROM AUTHOR]

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented.

In this paper, a new impulsive integro-differential inequality is presented, which can be widely applied to many fields in real world. Then, based on the equality, we analyze the exponential stability of some impulsive differential systems with discrete and continuously distributed delays, which illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of fault detection (FD) for networked control systems with discrete and infinite distributed delays subject to random packet losses and non‐linear perturbation. Both sensor‐to‐controller and controller‐to‐actuator packet losses are modelled as two different mutually independent Bernoulli distributed white sequences with known conditional probability distributions. By utilising an observer‐based fault detection filter (FDF) as a residual generator, the FD for networked non‐linear systems with mixed delays and packet losses is formulated as an H∞ model‐matching problem. Attention is focused on designing the FDF in the closed‐loop system setup such that the estimation error between the residuals and filtered faults is made as small as possible and at the same time the closed‐loop networked non‐linear system is exponentially stable in the mean‐square sense. To show the superiority and effectiveness of this work, two numerical examples are presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of passivity analysis for uncertain continuous-time neural networks with mixed time-varying delays. The mixed time-varying delays consist of both discrete and distributed delays, in which the discrete delays are assumed to be varying within a given interval. In addition, the uncertainties are assumed to be norm-bounded. By employing a novel Lyapunov–Krasovskii functional, new passivity delay-interval-dependent criteria are established to guarantee the passivity performance. When estimating an upper bound of the derivative of the Lyapunov–Krasovskii functional, we handle the terms related to the discrete and distributed delays appropriately so as to develop less conservative results. These passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved via standard numerical software. Some numerical examples are given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the global exponential synchronization of coupled connected neural networks with both discrete and distributed delays is investigated under mild condition, assuming neither the differentiability and strict monotonicity for the activation functions nor the diagonal for the inner coupling matrices. By employing a new Lyapunov–Krasovskii functional, applying the theory of Kronecker product of matrices and the linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions in LMI form are obtained for global exponential synchronization of such systems. Moreover, the decay rate is estimated. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using efficient Matlab LMI toolbox, and no tuning of parameters is required. In addition, the proposed results generalize and improve the earlier publications. An example with simulation is given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of stability analysis of neutral type neural networks with both discrete and unbounded distributed delays. In terms of linear matrix inequalities, delay-dependent conditions are obtained, which guarantee the considered delayed neural network to have a unique equilibrium point, which is globally asymptotically stable. Numerical examples are given to show the less conservatism and effectiveness of the proposed stability conditions. [Copyright &y& Elsevier]

Abstract: In this paper, the global asymptotic stability of neutral-type neural networks with unbounded distributed delays is analyzed by utilizing the Lyapunov–Krasovskii functional and the linear matrix inequality (LMI) approach. A new sufficient condition ensuring the global asymptotic stability for neutral-type neural networks is obtained by using the powerful MATLAB LMI toolbox. Two examples are provided to illustrate the applicability of the stability results. [Copyright &y& Elsevier]

Abstract: In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral type neural networks with distributed delays. In addition, the examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB. [Copyright &y& Elsevier]

By employing the Lyapunov-Krasovskii functional and linear matrix inequality (LMI) approach, the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time-varying delays and distributed time-varying delays. Some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time-varying delay. The proposed LMI result is computationally efficient as it can be solved numerically using standard commercial software. Two examples are given to show the usefulness of the results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a model of discrete delayed quaternion-valued neural networks with interval parameter uncertainties is considered. Some sufficient conditions for the existence, uniqueness and globally robust stability of the equilibrium point are obtained. The approach is on the basis of the homeomorphic mapping method, the Lyapunov stability theorem and inequality techniques. Finally, a numerical example is given to demonstrate the application of the obtained results.

In this article, the fixed-time synchronization for competitive neural networks (CNNs) with Gaussian-wavelet-type activation functions and discrete delays is investigated. Firstly, in terms of Lyapunov stability theory and inequality technique, simple synchronization conditions are obtained by designing some feedback controllers. Secondly, the activation functions adopted in CNNs are Gaussian-wavelet-type activation functions for the first time, which have great preponderance in network optimization and storage capacity. Furthermore, the settling time with upper bound of the system to achieve fixed-time synchronization can be explicitly evaluated, which is irrelevant to the initial value of the system. Finally, the theoretical results which we derived are attested to be indeed feasible in terms of two numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control on predator, the prey species still extinct, whereas the predator species is stable at certain values. Several examples are presented to show the feasibility of the main results.

We study a nonlinear functional differential model of an anaerobic digestion process of wastewater treatment with biogas production. The model equations of biomass include two different discrete time delays. A mathematical analysis of the model is completed including existence and local stability of nontrivial equilibrium points, existence and boundedness of the model solutions as well as global stabilizability towards an admissible equilibrium point. We propose and apply a numerical extremum seeking algorithm for maximizing the biogas flow rate in real time. Numerical simulation results are also included. [ABSTRACT FROM AUTHOR]

In this study, finite‐time synchronisation between two chaotic systems with discrete and distributed delays is investigated by using periodically intermittent memory feedback control. Based on finite‐time stability theory, some novel and effective synchronisation criteria of intermittent control are derived by means of linear matrix inequalities and differential inequality techniques. Furthermore, a necessary condition of finite‐time synchronisation of intermittent control is given for neural networks with discrete and distributed delays. A numerical example on two chaotic neural networks shows the effectiveness and correctness of the derived theoretical results. In addition, a secure communication synchronisation problem is presented to demonstrate practical effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species (pollinators or dispersers) that interacts with several plant species (flowering plants or fruit trees), or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals. [ABSTRACT FROM AUTHOR]

In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria. [ABSTRACT FROM AUTHOR]

We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation. [ABSTRACT FROM AUTHOR]