Leakage Delay Research Articles

Finite-time sampled-data synchronization for uncertain neutral-type semi-Markovian jump neural networks with mixed time-varying delays

This paper addresses the finite-time synchronization problem for neutral-type semi-Markovian jump neural networks subject to random occurred uncertainties by sampled-data control approach. In order to deal with the influence of leakage delay and additive time delays on neutral-type neural networks, an appropriate Lyapunov–Krasovskii functional is employed. Some sufficient conditions are presented to guarantee the stochastic finite-time synchronization of the master system and slave system with an L2−L∞ performance level. In terms of linear matrix inequalities, the sampled-data controller gains are obtained. Two numerical examples are provided to demonstrate the effectiveness of our proposed method.

DYNAMICS OF A FRACTIONAL-ORDER BAM NEURAL NETWORK WITH LEAKAGE DELAY AND COMMUNICATION DELAY

This paper lucubrates the bifurcations of a fractional-order bidirectional associative memory neural network (FOBAMNN) with leakage and communication delays. Firstly, leakage delay is taken as a bifurcation parameter to detect the bifurcations of the proposed neural network (NN). Leakage delay-induced bifurcation results are commendably established. Then communication delay is regarded as a bifurcation parameter to investigate the bifurcations of the developed FOBAMNN, and the stability interval and bifurcation point are derived. It reveals that the devised FOBAMNN possesses outstanding stability performance if selecting a lesser value of them, while the bifurcation emerges of FOBAMNN and eventually leads to performance deterioration with an outsize one. Besides, the influence of fractional order on the bifurcation points is carefully studied. It perceives that a proper fractional order can heighten the stability performance of the developed FOBAMNN. Ultimately, numerical simulations are exploited to underpin the developed theory.

Almost periodic synchronization of quaternion-valued fuzzy cellular neural networks with leakage delays

This paper mainly studies the synchronization issue of quaternion-valued fuzzy cellular neural networks (QVFCNNs) with leakage delays. To avoid non-commutativity, we decompose the QVFCNNs into an analogous real-valued system. Then, we investigate the existence of almost periodic solutions based on the Banach fixed point theorem. Also, a novel state-feedback controller is designed to guarantee the synchronization of the global exponential almost periodicity. Finally, two examples are given to illustrate the effectiveness of our results.

Bifurcation Properties for Fractional Order Delayed BAM Neural Networks

In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the stability and the existence of Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. The Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software will be applied. The stability condition and the sufficient criterion of existence of Hopf bifurcation for fractional order BAM neural networks with delay (leakage delay) are established. It is found that when the sum of two delays (leakage delay) crosses a critical value, then a Hopf bifurcation will appear. The obtained results play an important role in designing neural networks. Also the derived results are new and enrich the bifurcation theory of fractional order delayed differential equations.

Asynchronous finite-time state estimation for semi-Markovian jump neural networks with randomly occurred sensor nonlinearities

This paper addresses the finite-time state estimation problem for semi-Markovian jump neural networks with sensor nonlinearities under the consideration of leakage delay and time-varying delay. The modes of original system and desired estimator are supposed to be asynchronous. Some sufficient conditions are proposed to guarantee the finite-time boundedness as well as mixed H∞ and passive performance of the error system in terms of constructing Lyapunov–Krasovskii functionals. By utilizing affine Bessel-Legendre inequalities, a less conservative result can be achieved. By virtue of linear matrices inequalities approach, the asynchronous state estimator gains are obtained. Two numerical examples are provided to demonstrate the less conservativeness and effectiveness of our method.

Exponential stability analysis for discrete-time quaternion-valued neural networks with leakage delay and discrete time-varying delays

In this paper, we consider the issue of exponential stability analysis for discrete-time quaternion-valued neural networks(DTQVNNs) with leakage delay and discrete time-varying delays. The DTQVNNs are investigated directly rather than through real decomposition method or plural decomposition method. Firstly, the existence and uniqueness of the equilibrium point for DTQVNNs are proposed by using homeomorphic mapping theorem and Cauchy-Schwarz inequality. Then, based on Lyapuinov-Krasovskii functional and matrix inequality, a delay-dependent sufficient condition is provided to guarantee the exponential stability of the equilibrium point for DTQVNNs. Finally, a numerical example is utilized to illustrate the effectiveness of the obtained results.

Stability analysis of stochastic fractional-order competitive neural networks with leakage delay

This article, we explore the stability analysis of stochastic fractional-order competitive neural networks with leakage delay. The main objective of this paper is to establish a new set of sufficient conditions, which is for the uniform stability in mean square of such stochastic fractional-order neural networks with leakage. Specifically, the presence and uniqueness of arrangements and stability in mean square for a class of stochastic fractional-order neural systems with delays are concentrated by using Cauchy-Schwartz inequality, Burkholder-Davis-Gundy inequality, Banach fixed point principle and stochastic analysis theory, respectively. Finally, four numerical recreations are given to confirm the hypothetical discoveries.

Pseudo almost periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales

<abstract> This paper deals with a class of quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales. Based on the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for the considered networks. The results of this paper are completely new. Finally, an example is presented to illustrate the effectiveness of the obtained results. </abstract>

Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks

Abstract During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is rare. In this manuscript, we are to consider the stability and the existence of Hopf bifurcation of fractional-order complex-valued neural networks. By separating the coefficients and the activation functions into their real and imaginary parts and choosing the time delay as bifurcation parameter, we establish a set of sufficient conditions to ensure the stability of the equilibrium point and the existence of Hopf bifurcation for the involved network. The study shows that both the fractional order and the leakage delay have an important impact on the stability and the existence of Hopf bifurcation of the considered model. Some suitable numerical simulations are implemented to illustrate the pivotal theoretical predictions. At last, we ends this article with a simple conclusion.

Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays

This paper deals with the finite-time stabilization of uncertain static neural networks (USNNs) where impulsive effects, leakage delay and infinite distributed delay are taken into account. Firstly, two types of impulses containing stabilizing impulses (SI) and destabilizing impulses(DI) are considered. Secondly, the designed settling-time relies not just on initial conditions but also on impulse time sequences. Besides, the impulse inputs can be constructed such that a finite time stable system admits a desired upper bound on the settling-time. Finally, two numerical examples with graphical illustrations are provided to demonstrate the effectiveness of our theoretical main results.

Impulsive effect on fixed-time control for distributed delay uncertain static neural networks with leakage delay

Abstract In this paper, the problem of fixed-time stabilization (FXTSB) for an uncertain impulsive distributed delay static neural networks (UIDSNNs) with leakage delay is investigated. Firstly, a new memory controller distinct from the existing ones is build. Besides, by using new Lyapunov function which include a new vectorial function, some new criteria are established to deal with the impulsive effect on FXTSB of UIDSNNs with leakage. Under the proposed memory fixed-time controller, the average impulsive interval(AII)-dependent settling-time is established and the controller parameters can be expressed in the form of linear matrix inequalities (LMIs). Finally, some numerical examples with graphical illustrations are provided to demonstrate the effectiveness of our theoretical main results.

Global Stabilization of Memristive Neural Networks with Leakage and Time-Varying Delays Via Quantized Sliding-Mode Controller

This pape investigates the global stabilization of memristive neural networks (MNNs) with leakage and time-varying delays via quantized sliding-mode controller. The leakage delay is considered in the MNNs. Sliding mode controller is imported to ensure global stabilization of delayed MNNs. We also introduce two quantization schemes with uniform quantizer and logarithmic quantizer. Our goal is to deal with errors before and after quantization. We give some simulations and comparisons between two quantizers in the end of this paper.

Almost automorphic solutions for Clifford-valued neutral-type fuzzy cellular neural networks with leakage delays on time scales

We propose a class of Clifford-valued neutral-type fuzzy cellular neural network models with leakage delays on time scales, give the definition and basic properties of Clifford-valued almost automorphic functions on time scales, and prove a composition theorem of Clifford-valued almost automorphic functions on time scales, and on this basis, we study the existence and global exponential stability of almost automorphic solutions of this class of neural networks. The research in this paper can unify the research of real-valued neural networks, complex-valued neural networks and quaternion-valued neural networks, as well as the research of continuous-time neural networks and discrete-time neural networks. Finally, an example illustrates the feasibility of the results obtained.

Bifurcations in a fractional-order neural network with multiple leakage delays

This paper expatiates the stability and bifurcation for a fractional-order neural network (FONN) with double leakage delays. Firstly, the characteristic equation of the developed FONN is circumspectly researched by employing inequable delays as bifurcation parameters. Simultaneously the bifurcation criteria are correspondingly extrapolated. Then, unequal delays-spurred-bifurcation diagrams are primarily delineated to confirm the precision and correctness for the values of bifurcation points. Furthermore, it lavishly illustrates from the evidence that the stability performance of the proposed FONN can be demolished with the presence of leakage delays in accordance with comparative studies. Eventually, two numerical examples are exploited to underpin the feasibility of the developed theory. The results derived in this paper have perfected the retrievable outcomes on bifurcations of FONNs embodying unique leakage delay, which can nicely serve a benchmark deliberation and provide a comparatively credible guidance for the influence of multiple leakage delays on bifurcations of FONNs.

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

New convergence results on cellular neural networks with leakage delay and proportional delay

In the present work, we mainly focus on shunting inhibitory cellular neural networks (SICNNs) involving leakage delays and proportional delays. By applying the inequality technique, a novel sufficient criterion to ascertain the convergence of every solution of SICNNs with leakage delays and proportional delays is derived. Simulation results are delineated to substantiate the correctness of our theoretical findings. Up to now, very few scholars deal with the neural networks with leakage delays and proportional delays. The derived conclusion of this work is a novelty and supplements several earlier works.

Anti-synchronization for complex-valued neural networks with leakage delay and time-varying delays

This paper discusses the anti-synchronization control of complex-valued neural networks(CVNNs) with leakage delay and time-varying delays. Based on different types of activation functions meeting different assumption conditions, via some inequalities techniques and the Lyapunov approach, some sufficient conditions are acquired of the anti-synchronization of CVNNs by choosing the suitable controllers. Finally, two examples are presented to validate the effectiveness of the obtained criteria.

Weighted pseudo almost periodic solutions for Clifford-valued neutral-type neural networks with leakage delays on time scales

In this paper, we consider a class of Clifford-valued neutral-type neural networks with leakage delays on time scales. We do not decompose the networks under consideration into real-valued systems, but we directly study the Clifford-valued networks. We first establish the existence of weighted pseudo almost periodic solutions of this class of neural networks by the theory of calculus on time scales and the Banach fixed point theorem. Then, we study the global exponential stability of weighted pseudo almost periodic solutions of this class of neural networks by using inequality techniques and the proof by contradiction. Finally, we give an example to illustrate the feasibility of the obtained results.

Synchronization of delayed fractional-order complex-valued neural networks with leakage delay

This paper talks about the global synchronization of delayed fractional-order complex valued neural networks (FOCVNNs) with leakage delay. A new fractional differential inequality is proposed, which offers an important tool in the investigation of synchronization about FOCVNNs. Through constructing appropriate Lyapunov function and using the fractional order comparison theory, some new synchronization conditions are established. A numerical example is given to demonstrate the feasibility of the proposed method.

Generalized dissipativity state estimation for genetic regulatory networks with interval time-delay signals and leakage delays

This paper examines the state estimation issue of genetic regulatory networks (GRNs) including time delays and leakage delay term subject to unified dissipativity performance based on the Lyapunov functional approach. The main aim of the proposed state estimator is to access the true concentrations of the proteins and mRNAs, which is explored based on the available output measurements. As a first attempt, the generalized dissipativity concept is implemented for GRNs to generalizing the state estimation technique in the framework of linear matrix inequalities (LMIs) via an improved integral inequality together with the reciprocally convex inequality (RCI) technique. Then, the developed criterion ensures that the estimated error dynamics to be asymptotically stable and extended dissipative in addition to well monitored by the original dynamics via unified dissipativity performance. Finally, an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in Escherichia coli is illustrated to explore the effectiveness and applicability of the developed state estimation technique, along with a comparison study also been exploited by using widely studied example.