Biomedical subjects

Jinde Cao

Publications and source records attributed to Jinde Cao.

15 recordsLinked to original sources

PubMed2006

Global point dissipativity of neural networks with mixed time-varying delays.

By employing the Lyapunov method and some inequality techniques, the global point dissipativity is studied for neural networks with both discrete time-varying delays and distributed time-varying delays. Simple sufficient conditions are given for checking the global point dissipativity of neural networks with mixed time-varying delays. The proposed linear matrix inequality approach is computationally efficient as it can be solved numerically using standard commercial software. Illustrated examples are given to show the usefulness of the results in comparison with some existing results.

Action Potentials↗

PubMed2006

Adaptive synchronization of neural networks with or without time-varying delay.

In this paper, based on the invariant principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the synchronization of almost all kinds of coupled identical neural networks with time-varying delay, which can be chaotic, periodic, etc. We do not assume that the concrete values of the connection weight matrix and the delayed connection weight matrix are known. We show that two coupled identical neural networks with or without time-varying delay can achieve synchronization by enhancing the coupling strength dynamically. The update gain of coupling strength can be properly chosen to adjust the speed of achieving synchronization. Also, it is quite robust against the effect of noise and simple to implement in practice. In addition, numerical simulations are given to show the effectiveness of the proposed synchronization method.

Action Potentials↗

PubMed2006

Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks.

In this paper, a new type of generalized Q-S (lag, anticipated, and complete) time-varying synchronization is defined. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks have been considered, where the delays are multiple time-varying delays. A novel control method is given by using the Lyapunov functional method. With this new and effective method, parameters identification and Q-S (lag, anticipated, and complete) time-varying synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.

Action Potentials↗

PubMed2006

Solving quadratic programming problems by delayed projection neural network.

In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

Algorithms↗

PubMed2006

Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays.

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.

Algorithms↗

PubMed2006

Robust stability of switched Cohen-Grossberg Neural networks with mixed time-varying delays.

By combining Cohen-Grossberg neural networks with an arbitrary switching rule, the mathematical model of a class of switched Cohen-Grossberg neural networks with mixed time-varying delays is established. Moreover, robust stability for such switched Cohen-Grossberg neural networks is analyzed based on a Lyapunov approach and linear matrix inequality (LMI) technique. Simple sufficient conditions are given to guarantee the switched Cohen-Grossberg neural networks to be globally asymptotically stable for all admissible parametric uncertainties. The proposed LMI-based results are computationally efficient as they can be solved numerically using standard commercial software. An example is given to illustrate the usefulness of the results.

Journal Article↗

PubMed2006

A delayed neural network method for solving convex optimization problems.

In this paper, the delayed projection neural network for a class of solving convex programming problem is proposed. The existence of solution and global exponential stability of the proposed network are proved, which can guarantee to converge at an exact optimal solution of the convex programming problems. Several examples are given to show the effectiveness of the proposed network.

Algorithms↗

PubMed2005

New conditions for global exponential stability of cellular neural networks with delays.

In this paper, we study further a class of cellular neural networks model with delays. By employing the inequality api(m)(k=1)1 b(q(k))(k) or=0, b(k) >or=0, q(k) > 0 with sigma(m)(k=1) q(k) = r-1, and r > 1), constructing a new Lyapunov functional, and applying the Homeomorphism theory, we derive some new conditions ensuring the existence, uniqueness of the equilibrium point and its global exponential stability for cellular neural networks. These conditions are independent of delays and possess infinitely adjustable real parameters, which are of highly important significance in the designs and applications of networks. In addition, we extend or improve the previously known results.

Algorithms↗

PubMed2005

Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters.

This paper studies the adaptive complete synchronization of chaotic and hyperchaotic systems with fully unknown parameters. In practical situations, some systems' parameters cannot be exactly known a priori, and the uncertainties often affect the stability of the process of synchronization of the chaotic oscillators. An adaptive scheme is proposed to compensate for the effects of parameters' uncertainty based on the structure of chaotic systems in this paper. Based on the Lyapunov stability theorem, an adaptive controller and a parameters update law can be designed for the synchronization of chaotic and hyperchaotic systems. The drive and response systems can be nonidentical, even with different order. Three illustrative examples are given to demonstrate the validity of this technique, and numerical simulations are also given to show the effectiveness of the proposed chaos synchronization method. In addition, this synchronization scheme is quite robust against the effect of noise.

Adaptation, Physiological↗

PubMed2005

A delayed neural network for solving linear projection equations and its analysis.

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.

Algorithms↗

PubMed2004

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays.

In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems.

Algorithms↗

PubMed2004

Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays.

This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapunov function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.

Algorithms↗

PubMed2003

Global and robust stability of interval Hopfield neural networks with time-varying delays.

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.

Algorithms↗

PubMed2003

Novel stability criteria for delayed cellular neural networks.

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.

Algorithms↗

PubMed1998

Stability analysis of delayed cellular neural networks.

In this paper, the problems of stability in a class of delayed cellular neural networks (DCNN) are studied; some new stability criteria are obtained by using the Lyapunov functional method and some analysis techniques. These criteria can be used to design globally stable networks and thus have important significance in both theory and application.

Journal Article↗