On affine state-space neural networks for system identification: Global stability conditions and complexity management

2013 ◽  
Vol 21 (4) ◽  
pp. 518-529 ◽  
Author(s):  
P. Gil ◽  
J. Henriques ◽  
A. Cardoso ◽  
A. Dourado
Keyword(s):  
Neural Networks ◽  
System Identification ◽  
Global Stability ◽  
State Space ◽  
Stability Conditions ◽  
Complexity Management

Global Stability Analysis for Complex-Valued Recurrent Neural Networks and Its Application to Convex Optimization Problems

2009 ◽  
pp. 104-122 ◽  
Author(s):  
Mitsuo Yoshida ◽  
Takehiro Mori
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Global Stability ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Continuous Time ◽  
Stability Conditions ◽  
Global Stability Analysis ◽  
Solution Methods ◽  
Complex Valued

Global stability analysis for complex-valued artificial recurrent neural networks seems to be one of yet-unchallenged topics in information science. This chapter presents global stability conditions for discrete-time and continuous- time complex-valued recurrent neural networks, which are regarded as nonlinear dynamical systems. Global asymptotic stability conditions for these networks are derived by way of suitable choices of activation functions. According to these stability conditions, there are classes of discrete-time and continuous-time complex-valued recurrent neural networks whose equilibrium point is globally asymptotically stable. Furthermore, the conditions are shown to be successfully applicable to solving convex programming problems, for which real field solution methods are generally tedious.

scholarly journals Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey

Diversity ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 23
Author(s):  
Jawdat Alebraheem
Keyword(s):  
Global Stability ◽  
Stability Conditions ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model.

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