Convergence Analysis of Recurrent Neural Networks

Zhang, Yi

doi:10.1007/978-1-4757-3819-3

Cited by 72 publications

(34 citation statements)

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“…Since (x(t), S(t)) is bounded, by using the same arguments appeared in [12,13], this theorem can be proved easily.…”

Section: Complete Convergencementioning

confidence: 84%

“…It is well known that the activation functions are important factors affecting the dynamic behavior of neural networks. Neural networks with unsaturated linear activation functions have got extensive interest recently, see for examples [2,4,5,10,12,13]. Such neural networks have potential importance in many applications.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], it is pointed out that such neural networks are computationally restrictive which cannot deal with some important neural computations such as decision making. Recently, there has been increasing interest in multiple equilibrium points case, see [4,5,10,12,13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Complete Convergence of Competitive Neural Networks with Different Time Scales

Zhang

2005

Neural Process Lett

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This paper studies the complete convergence of a class of neural networks with different time scales under the assumption that the activation functions are unsaturated piecewise linear functions. Under this assumption, there are multiple equilibrium points in the neural network. Traditional methods cannot be used in this neural network. Complete convergence is proved by constructing an energy-like function. Simulations are employed to illustrate the theory.

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“…Since (x(t), S(t)) is bounded, by using the same arguments appeared in [12,13], this theorem can be proved easily.…”

Section: Complete Convergencementioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complete Convergence of Competitive Neural Networks with Different Time Scales

Zhang

2005

Neural Process Lett

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“…Obviously, the algorithms have many equilibria and, thus, the study of dynamics belongs to a multistability problem [27]. According to the Lyapunov indirect method, an equilibrium of an algorithm is stable if the absolute of each eigenvalue of the Jacobian matrix of the algorithm at this point is less than 1 [16].…”

Section: Definition 3 a Point W * ∈ R N Is Called An Equilibrium Of (mentioning

confidence: 99%

Stability and Chaos of a Class of Learning Algorithms for ICA Neural Networks

Tan

Zhang

et al. 2008

Neural Process Lett

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Independent component analysis (ICA) neural networks can estimate independent components from the mixed signal. The dynamical behavior of the learning algorithms for ICA neural networks is crucial to effectively apply these networks to practical applications. The paper presents the stability and chaotic dynamical behavior of a class of ICA learning algorithms with constant learning rates. Some invariant sets are obtained so that the non-divergence of these algorithms can be guaranteed. In these invariant sets, the stability and chaotic behaviors are analyzed. The conditions for stability and chaos are derived. Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior.

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“…But in many real applications, biological systems are no longer globally stable, thus more appropriate notions of stability are needed to deal with multistable networks. Yi and Tan (2004) investigated three important properties: boundedness, attractivity and complete convergence of a multistable networks. Liao and Wang (2003) addressed the global dissipativity of a general class of continuous-time recurrent neural networks.…”

Section: Introductionmentioning

confidence: 99%

Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

2010

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In this paper, the global exponential stability in Lagrange sense for genetic regulatory networks (GRNs) with SUM regulatory logic is firstly studied. By constructing appropriate Lyapunov-like functions, several criteria are presented for the boundedness, ultimate boundedness and global exponential attractivity of GRNs. It can be obtained that GRNs with SUM regulatory logic are unconditionally globally exponentially stable in Lagrange sense. These results can be applied to analyze monostable as well as multistable networks. Furthermore, to analyze the stability for GRNs more comprehensively, the existence of equilibrium point of GRNs is proved, and some sufficient conditions of the global exponential stability in Lyapunov sense for GRNs are derived. Finally two numerical examples are given to illustrate the application of the obtained results.

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Convergence Analysis of Recurrent Neural Networks

Cited by 72 publications

References 0 publications

Complete Convergence of Competitive Neural Networks with Different Time Scales

Complete Convergence of Competitive Neural Networks with Different Time Scales

Stability and Chaos of a Class of Learning Algorithms for ICA Neural Networks

Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

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