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In this paper, we analyze the global asymptotic stability and global exponential stability with respect to the Clifford-valued neutral-type neural network (NN) models with time delays. By considering the neutral term, a Clifford-valued NN model with time delays is formulated, which encompasses real-valued, complex-valued, and quaternion-valued NN models as special cases. In order to achieve our main results, the n -dimensional Clifford-valued NN model is decomposed into 2 m n -dimensional real-valued models. Moreover, a proper function is constructed to handle the neutral term and prove that the equilibrium point exists. Utilizing the homeomorphism theory, linear matrix inequality as well as Lyapunov functional methods, we derive the sufficient conditions corresponding to the existence, uniqueness, and global asymptotic stability with respect to the equilibrium point of the Clifford-valued neutral-type NN model. Numerical examples to demonstrate the effectiveness of the results are provided, and the simulations results are analyzed and discussed.

In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

This paper investigates the problem of finite-/fixed-time synchronization for Clifford-valued recurrent neural networks with time-varying delays. The considered Clifford-valued drive and response system models are firstly decomposed into real-valued drive and response system models in order to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers. Then, suitable time-delayed feedback controllers are devised to investigate the synchronization problem in finite-/fixed-time of error system. On the basis of new Lyapunov–Krasovskii functional and new computational techniques, finite-/fixed-time synchronization criteria are formulated for the corresponding real-valued drive and response system models. Two numerical examples demonstrate the effectiveness of the theoretical results.

This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into $2^{m}n$ 2 m n real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications.

This work investigates the finite-time event-triggered approach for recurrent neural networks with leakage term and its application. Here, decentralized event-triggered framework is recommended where event is checked at every sensor node related to local information for available triggering and the updated control is done whenever a centralized event is triggered. By handling the Lyapunov–Krasovskii functional (LKF) method together with novel inequality techniques like Wirtinger single and double integral inequality (WSI,WDI) technique, delay productive term (DPT), and a few adequate conditions are acquired to ensure the finite-time stability (FTS) analysis for the considered system, which is expressed with respect to linear matrix inequalities (LMIs). At last, numerical simulations are provided to indicate the efficiency of the expected results, two of these examples were supported by genuine use of the benchmark issue that correlates with sensible concerns under finite-time execution.

This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1 , i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.

In this paper, we focus on the global stability analysis with respect to dynamical delayed neural networks (NNs) that contain parameter uncertainties. Many investigations on the sufficient conditions utilizing different upper bounds for the norm of interconnection matrices pertaining to the global asymptotic robust stability of delayed NNs have been conducted. In this study, a new upper bound of the norm of connection weight matrices is derived for the delayed NNs under parameter uncertainties. The key focus is on how the new upper bound is able to yield minimum result with respects to some of the existing upper bounds. We demonstrate that the new upper bound can lead to some new sufficient conditions with respect to the global asymptotic robust stability of equilibrium point of the delayed NNs. The slope bounded activation functions and Lyapunov-Krasovskii functionals (LKFs) are employed for formulating the sufficient conditions of the equilibrium point of NNs. Moreover, the derived sufficient conditions are independent on the time delay parameter. Numerical examples are provided and the outcomes obtained are compared with those of the existing results subject to different network parameters.

We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations.

The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order $$0

This manuscript prospects the controllability criteria of non-instantaneous impulsive Volterra type fractional differential systems. By enroling an appropriate Gramian matrix that is often defined by the Mittag-Leffler function and with the assistance of Laplace transform, the necessary and sufficiency conditions for the controllability of non-instantaneous impulsive Volterra-type fractional differential equations are derived by using algebraic approach and Cayley–Hamilton theorem. An important feature present in our paper is that we have taken non-instantaneous impulses into the fractional order dynamical system and studied the controllability analysis, since this do not exist in the available source of literature. Inclusively, we have provided two illustrative examples with the existence of non-instantaneous impulse into the fractional dynamical system. So this demonstrates the validity and efficacy of our obtained criteria of the main section.

Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.

This paper concerns with the problem of exponential stability analysis of time-delayed recurrent neural networks with impulsive and stochastic effects under fractional segments or intervals in delays. The delays in discrete term are assumed to be time-varying and different from existing literature, the discrete delay interval has been separated into fractional segments, which guarantees the availability of lower and upper bounds for feasibility with accuracy. By constructing a suitable Lyapunov–Krasovskii functional (LKF), with the aid of stability theory and inequality techniques, several novel criteria are originated via linear matrix inequalities (LMIs) to ensure the exponential stability of addressed neural networks in the mean square sense. Finally, two numerical examples are presented to substantiate the superiority and effectiveness of our theoretical outcomes.

This manuscript is perturbed with a controllability problem of nonlinear fractional dynamical systems with delay in the state variable. By employing Laplace transformation technique and using Mittag-Leffler function, solution representation of the examined fractional delay differential equations can be devised. Besides, we build the necessary as well as sufficient condition, in order to prove the controllability of linear fractional delay dynamical structures. Especially, the sufficiency part for the controllability results is obtained by using the fixed point argument. In addition to that, we have provided three numerical examples to illustrate the essence of our obtained theoretical statements.

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the originaln-dimensional Clifford-valued model into$2^{m}n$2mn-dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.

Dynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II, while the interaction between the intermediate and top predators follows the Crowley–Martin functional response. The local stability and bifurcation analysis of the proposed model at the interior equilibrium point are studied. Numerical simulations are provided to ensure the mathematical results.

The problem of finite-time stability of switched genetic regulatory networks (GRNs) with time-varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities (LMIs) are established for finite-time stability of switched GRNs. The applicability of the developed finite-time stability conditions is validated by numerical results.

This study aims to use the fractional Fourier transform for analyzing various types of Hyers–Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers–Ulam–Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.

In the current study, we conduct an investigation into the Hyers–Ulam stability of linear fractional differential equation using the Riemann–Liouville derivatives based on fractional Fourier transform. In addition, some new results on stability conditions with respect to delay differential equation of fractional order are obtained. We establish the Hyers–Ulam–Rassias stability results as well as examine their existence and uniqueness of solutions pertaining to nonlinear problems. We provide examples that indicate the usefulness of the results presented.

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

Stochastic disturbances often cause undesirable characteristics in real-world system modeling. As a result, investigations on stochastic disturbances in neural network (NN) modeling are important. In this study, stochastic disturbances are considered for the formulation of a new class of NN models, i.e., the discrete-time stochastic quaternion-valued neural networks (DSQVNNs). In addition, the mean-square asymptotic stability issue in DSQVNNs is studied. Firstly, we decompose the original DSQVNN model into four real-valued models using the real-imaginary separation method, in order to avoid difficulties caused by non-commutative quaternion multiplication. Secondly, some new sufficient conditions for the mean-square asymptotic stability criterion with respect to the considered DSQVNN model are obtained via the linear matrix inequality (LMI) approach, based on the Lyapunov functional and stochastic analysis. Finally, examples are presented to ascertain the usefulness of the obtained theoretical results.

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system&rsquo, s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov&ndash, Krasovskii functional and applying Jensen&rsquo, s inequality, a number of sufficient conditions can be derived by utilizing It o ^ &rsquo, s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

This paper analyzes the robust dissipativity of uncertain stochastic generalized neural networks (USGNNs) with Markovian jumping parameters and time-varying delays. In practical applications most of the systems refer to uncertainties, hence, the norm-bounded parameter uncertainties and stochastic disturbance are considered. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and by employing integral inequalities LMI-based sufficient conditions of the considered systems are established. Numerical simulations are given to show the merit of the presented results.

This paper studies the global Mittag&ndash, Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag&ndash, Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts.

In this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.

In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov–Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

In this work, we probes the stability results of H∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.

This proposal analyzes the problem of asymptotic approach on stability criteria for impulsive discrete-time BAM neural networks with random parameter uncertainties and time-varying leakage delays. Reciprocally convex combination technique is approached in this paper for the reduction of decision variables. This lemma is derived from the derivation of Jensen’s inequality. Here, the uncertainties are considered as a randomly occurring parameter uncertainty and it obey certain mutually uncorrelated Bernoulli-distributed white noise sequences. A priori indicates the occurrence of uncertain parameters in the probability which is the valuable feature. Some novelty sufficient conditions for ensuring the asymptotic stability of the addressed neural networks are attained in terms of linear matrix inequalities (LMIs) by the aid of Lyapunov–Krasovskii functionals approach, which can be easily checked by MATLAB LMI Toolbox. Finally, three illustrative examples are accomplished to manifest the effectiveness and fruitfulness of the proposed research work.

In this paper, we focus on the global asymptotic stability problem for Clifford-valued neural network models with time-varying delays as well as impulsive effects. By considering impulsive effects, a general class of network model is considered, which encompasses real-valued, complex-valued, and quaternion-valued neural network models as special cases. Firstly, the n -dimensional Clifford-valued model is decomposed into 2 m n -dimensional real-valued model, which avoids non-commutativity of multiplication of Clifford numbers. Based on the Lyapunov stability theory, contraction mapping principle, and some mathematical concepts, we derive the existence, uniqueness of the equilibrium point with respect to the model. New sufficient conditions are also derived, in order to ensure the global asymptotic stability of the considered model. To illustrate the usefulness of the obtained results, a simulation example is presented.

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff&rsquo, s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

This paper deals with finite-time stability and stabilization problem of singular linear discrete-time systems with time-varying delay and norm-bounded disturbance. We first present novel delay-dependent sufficient conditions for the robust finite-time stability of the system. Then the results are applied to solve finite-time stabilization problem of linear singular discrete-time control delay systems. The conditions are presented in terms of linear matrix inequalities, which can be determined by utilizing MATLABs LMI Control Toolbox. The effectiveness of the results are illustrated by numerical examples.

This note pays precise attention to derive the γ-exponential stability results of positive delayed systems via non-fragile control. By using Lyapunov–Krasovskii theory some necessary conditions are derived. Moreover, by using results from spectrum analysis the sufficient conditions for positive delayed systems with non-fragile control are analyzed. Our main intension is to locate the ideal application of this type of systems. In later part of this paper, the novel mathematical model which describes the life stages of Aedes Aegypti mosquitoes is proposed. In that model, the life shorting bacteria called Wolbachia is used as a biological control. By moderately thinking about the uncertain conditions in the biological control we implemented the non-fragile control. By applying the proposed results the γ-exponential stability of this population system is derived. Finally, some numerical examples are provided to expose the effectiveness of our predominant results.

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ &rsquo, s formula, Dynkin&rsquo, s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system&rsquo, s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen’s inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.

This paper is concerned with asymptotic stability and stabilization of nonlinear uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the nonlinear uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.