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1.
The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach. 相似文献
2.
Global stability of population models 总被引:2,自引:0,他引:2
Paul Cull 《Bulletin of mathematical biology》1981,43(1):47-58
Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition
for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability
to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then
the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions
of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a
method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions. 相似文献
3.
This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results. 相似文献
4.
R. Suresh Kumar G. Sugumaran R. Raja Quanxin Zhu U. Karthik Raja 《Cognitive neurodynamics》2016,10(1):85-98
This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov–Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature. 相似文献
5.
Designing a network with given functions or reconstruct a network based on its dynamical behavior is an important problem in the study of complex systems. In this paper, we put forward certain principles in constructing a network with state stability. We show that a necessary and sufficient condition to design networks with a global fixed point is that active nodes inhibit inactive nodes, while the latter activate the former directly or indirectly. We also designed networks based on basic modules, where each basic module consists a sub-network, they communicate through the inhibition link from each activator in lower module to the inhibitor of upper module. We found that long activation links, i.e. indirect activation links are important to the formation of convergence trajectory. We believe that these principles may help us to understand the topology of biological networks. 相似文献
6.
In this paper, the global robust stability problem of delayed Takagi–Sugeno fuzzy Hopfield neural networks with discontinuous
activation functions (TSFHNNs) is considered. Based on Lyapunov stability theory and M-matrices theory, we derive a stability criterion to guarantee the global robust stability of TSFHNNs. Compared with the existing
literature, we remove the assumptions on the neuron activations such as Lipschitz conditions, bounded, monotonic increasing
property or the assumption that the right-limit value is bigger than the left one at the discontinuous point. Finally, two
numerical examples are given to show the effectiveness of the proposed stability results. 相似文献
7.
In this paper, we consider the global stability of the models which incorporate humoural immunity or cell-mediated immunity. We consider the effect of loss of a pathogen, which is called the absorption effect when it infects an uninfected cells. We construct Lyapunov functions for these models under some conditions of parameters, and prove the global stability of the interior equilibria. It is impossible to remove the condition of parameters for the model incorporating humoural immunity. 相似文献
8.
In this paper, a new sufficient condition is given for the global asymptotic stability and global exponential output stability of a unique equilibrium points of delayed cellular neural networks (DCNNs) by using Lyapunov method. This condition imposes constraints on the feedback matrices and delayed feedback matrices of DCNNs and is independent of the delay. The obtained results extend and improve upon those in the earlier literature, and this condition is also less restrictive than those given in the earlier references. Two examples compared with the previous results in the literatures are presented and a simulation result is also given. 相似文献
9.
Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here. 相似文献
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Gerd Rosenkranz 《Mathematical biosciences》1983,64(2):227-231
A necessary and sufficient condition for the global stability of a large class of discrete population models is provided which does not require the construction of a Liapunov function. The general result is applied to difference equations defined in terms of “two hump” functions and to an example of frequency dependent selection. 相似文献
13.
This paper considers the robust stability of a class of neural networks with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov-Krasovskii functional, a sufficient condition for the global exponential stability of the delayed Markovian jumping neural networks is established. The proposed condition is also extended to the uncertain cases, which are shown to be the improvement and extension of the existing ones. Finally, the validity of the results are illustrated by an example. 相似文献
14.
The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach. 相似文献
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利用分析技巧,获得了一类带有阈的神经网络模型全局稳定性的判据,去掉了文「1」相应结果的一个较强条件∫^∞0sk(s)ds〈+∞。 相似文献
18.
This paper investigates drive-response synchronization for a class of
neural networks with time-varying discrete and distributed delays (mixed delays) as
well as discontinuous activations. Strict mathematical proof shows the global
existence of Filippov solutions to neural networks with discontinuous activation
functions and the mixed delays. State feedback controller and impulsive controller
are designed respectively to guarantee global exponential synchronization of the
neural networks. By using Lyapunov function and new analysis techniques, several new
synchronization criteria are obtained. Moreover, lower bound on the convergence rate
is explicitly estimated when state feedback controller is utilized. Results of this
paper are new and some existing ones are extended and improved. Finally, numerical
simulations are given to verify the effectiveness of the theoretical results. 相似文献
19.
在全球变化背景下, 生态系统能否长期有效地维持功能并提供服务, 有赖于其稳定性。生态系统稳定性及其与生物多样性的关系, 是生态学研究的核心问题, 生物多样性能否促进生态系统稳定性曾引起很多争论。该文在前期国内外综述和研究的基础上, 重点从以下三个方面对近期进展做了总结。第一, 介绍了近期理论研究在生态系统稳定性的内涵及不同稳定性指标间的内在关联方面取得的新认识。第二, 梳理了最近基于生物多样性实验开展的多项整合分析研究和理论探索, 以及在多维度框架下开展的多样性-稳定性关系研究。第三, 详细介绍了最近发展起来的多尺度稳定性理论框架, 对稳定性的尺度依赖、多样性-稳定性的多尺度关系等新议题做了探讨。最后, 提出了本领域有待进一步研究的关键问题和方向建议。 相似文献
20.
We investigate the stability of Lotka-Volterra (LV) models constituted by two groups of species such as plants and animals in terms of the intragroup effective competition matrix, which allows separating the equilibrium equations of the two groups. In matrix analysis, the effective competition matrix represents the Schur complement of the species interaction matrix. It has been previously shown that the main eigenvalue of this effective competition matrix strongly influences the structural stability of the model ecosystem. Here, we show that the spectral properties of the effective competition matrix also strongly influence the dynamical stability of the model ecosystem. In particular, a necessary condition for diagonal stability of the full system, which guarantees global stability, is that the effective competition matrix is diagonally stable, which means that intergroup interactions must be weaker than intra-group competition in appropriate units. For mutualistic or competitive interactions, diagonal stability of the effective competition is a sufficient condition for global stability if the inter-group interactions are suitably correlated, in the sense that the biomass that each species provides to (removes from) the other group must be proportional to the biomass that it receives from (is removed by) it. For a non-LV mutualistic system with saturating interactions, we show that the diagonal stability of the corresponding LV system close to the fixed point is a sufficient condition for global stability. 相似文献