Finite-time stability of neutral-type neural networks with random time-varying delays

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov–Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.     

Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin’s continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained.     

Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays

This paper investigates the global asymptotic stability problem for a class of neutral-type complex-valued neural networks with random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the information of time-varying delay is assumed to be random time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing inequality technique, several sufficient conditions are obtained to ensure the global asymptotically stability of equilibrium point for the considered neural networks. The obtained stability criterion is expressed in terms of complex-valued linear matrix inequalities, which can be simply solved by effective YALMIP toolbox in MATLAB. Finally, three numerical examples are given to demonstrate the efficiency of the proposed main results.     

Global Asymptotic Stability of Periodic Solutions for Neutral-Type Delayed BAM Neural Networks by Combining an Abstract Theorem of k-Set Contractive Operator with LMI Method

Neural Processing Letters - The paper considers the existence and global asymptotic stability of periodic solutions for a class of neutral-type BAM neural networks with time delays. By combining an...     

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.     

Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays

This paper is concerned with a class of neutral-type neural networks with discontinuous activations and time-varying delays. Under the concept of Filippov solution, by applying the differential inclusions and the topological degree theory in set-valued analysis, we employ a novel argument to establish new results on the existence of the periodic solutions for the considered neural networks. After that, we derive some criteria on the uniqueness, global exponential stability of the considered neural networks and convergence of the corresponding autonomous case of the considered neural networks, in terms of nonsmooth analysis theory with Lyapunov-like approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, the results obtained can also be valid. Our results extend previous works on the neutral-type neural networks to the discontinuous cases, some related results in the literature can be enriched and extended. Finally, two typical examples and the corresponding numerical simulations are provided to show the effectiveness and flexibility of the results derived in this paper.     

Adaptive exponential synchronization in pth moment of neutral-type neural networks with time delays and Markovian switching

In this letter, the analysis problem of adaptive exponential synchronization in pth moment is considered for neutral-type neural networks with time delays and Markovian switching. By utilizing a new nonnegative function and the M-matrix approach, several sufficient conditions to ensure the adaptive exponential synchronization in pth moment for neutral-type neural networks are derived. Via the adaptive feedback control techniques, some suitable parameters update laws are found. To illustrate the effectiveness of the M-matrix-based synchronization conditions derived in this letter, numerical example is provided finally.     

Global exponential stability for neutral-type BAM neural networks with time-varying delays

In this article, the global exponential stability of neutral-type bidirectional associative memory (BAM) neural networks with time-varying delays is analysed by utilizing the Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach. New sufficient conditions ensuring the global exponential stability of neutral-type BAM neural networks is obtained by using the powerful MATLAB LMI control toolbox. In addition, an example is provided to illustrate the applicability of the result.     

New stability results of neutral-type neural networks with continuously distributed delays and impulses

This paper studies the globally asymptotic stability of neutral-type impulsive neural networks with discrete and bounded continuously distributed delays. By using the Lyapunov functional method, quadratic convex combination approach, a novel Gu's Lemma, Jensen integral inequality and linear convex combination technique, several novel sufficient conditions are derived to ensure the globally asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses

In this paper, the problem of neutral-type impulsive bidirectional associative memory neural networks (NIBAMNNs) with time delays are first established by a Takagi-Sugeno (T-S) fuzzy model in which the consequent parts are composed of a set of NIBAMNNs with interval delays and Markovian jumping parameters (MJPs). Sufficient conditions to check the robust exponential stability of the derived model are based on the Lyapunov-Krasovskii functionals (LKFs) containing some novel triple integral terms, Lyapunov stability theory and employing the free-weighting matrix method. The delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs), which can be very efficiently solved using Matlab LMI control toolbox. Finally, numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results.     

Multiple asymptotical stability analysis for fractional-order neural networks with time delays

This paper formulates the multiple asymptotical stability for a general class of fractional-order neural networks with time delays. By exploiting the properties of upper bounded and lower bounded functions derived from the addressed fractional-order neural network model as well as the comparison principle for fractional-order calculus, a lot of sufficient conditions are obtained to guarantee the existence and multiple asymptotical stability of the equilibrium points for the fractional-order neural networks with time delays. It reveals that the results gained in this paper are applicable to analyses of both multiple asymptotical stability and global asymptotical stability. Besides, three numerical examples are presented to showcase the validity of the derived results.     

Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays,distributed delays and time-varying delay in leakage delays

This paper is concerned with a class of neutral-type competitive neural networks with multi-proportional delays, distributed delays and leakage delays. By employing the differential inequality theory, some sufficient conditions are given to ensure that all solutions of the addressed system converge exponentially to zero vector. An illustrative example is also given at the end of this paper to show the effectiveness of our results.     

Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays

This paper deals with the robust stability problem of uncertain stochastic neural networks of neutral-type with interval time-varying delays. The uncertainties under consideration are norm-bounded, and the delay is assumed to be time-varying and belongs to a given interval. By using the Lyapunov-Krasovskill functional method and the linear matrix inequality (LMI) technique, the novel stability criteria are derived in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed criteria.     

Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays

In this paper, we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. Sufficient conditions are derived for ascertaining the existence, uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method. The periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays.     

Global robust stability of delayed neural networks with a class of general activation functions

In this paper, the global robust stability is discussed for delayed neural networks with a class of general activation functions. By constructing new Lyapunov functionals, several novel conditions are derived to guarantee the existence, uniqueness and global robust stability of the equilibrium of neural networks with time delays. These conditions do not require the activation functions to be differentiable, bounded or monotonically nondecreasing. The results obtained here are generalizations of some earlier results reported in the literature for neural networks with time delays. In addition, two examples are given to illustrate our proposed results.     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality

This paper investigates the stochastic stability problem for a class of neutral-type Markov jump neural networks with additive time-varying delays. Firstly, to derive a tighter lower bound of the reciprocally convex quadratic terms, a new reciprocally convex combination inequality is established by using parameters transformation approach. Secondly, by fully considering the peculiarity of various time-varying delays and Markov jumping parameters, an eligible stochastic Lyapunov–Krasovskii functional is constructed. Then, by employing the new reciprocally convex combination inequality and other analytical techniques, some novel stability criteria are provided in the forms of linear matrix inequalities. Finally, four illustrated examples are given to verify the effectiveness and feasibility of the proposed methods.     

The globally asymptotic stability analysis for a class of recurrent neural networks with delays

This paper considers the problem of global stability of neural networks with delays. By combining Lie algebra and the Lyapunov function with the integral inequality technique, we analyze the globally asymptotic stability of a class of recurrent neural networks with delays and give an estimate of the exponential stability. A few new sufficient conditions and criteria are proposed to ensure globally asymptotic stability of the equilibrium point of the neural networks. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.