Periodic oscillation for a complex-valued neural network model with discrete and distributed delays

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Chunhua Feng
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Sufficient Conditions ◽  
Periodic Oscillation ◽  
Activation Function ◽  
Distributed Delays ◽  
Oscillatory Solutions ◽  
Complex Valued ◽  
Theoretical Results

In this paper, a complex-valued neural network model with discrete and distributed delays is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established. Computer simulation is given to illustrate the validity of the theoretical results.

scholarly journals An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 19291-19302 ◽  
Author(s):  
Lei Ding ◽  
Lin Xiao ◽  
Kaiqing Zhou ◽  
Yonghong Lan ◽  
Yongsheng Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Neural Network Model ◽  
Sylvester Equation ◽  
Time Varying ◽  
Complex Valued

scholarly journals General Recurrent Neural Network for Solving Generalized Linear Matrix Equation

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Zhan Li ◽  
Hong Cheng ◽  
Hongliang Guo
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Neural Network Model ◽  
Matrix Equation ◽  
Activation Function ◽  
Linear Matrix ◽  
Activation Functions ◽  
State Matrix ◽  
Linear Matrix Equation

This brief proposes a general framework of the nonlinear recurrent neural network for solving online the generalized linear matrix equation (GLME) with global convergence property. If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can globally and exponentially converge to the unique theoretical solution of GLME. Additionally, as compared with the case of using the linear activation function, two specific types of nonlinear activation functions are proposed for the general nonlinear recurrent neural network model to achieve superior convergence. Illustrative examples are shown to demonstrate the efficacy of the general nonlinear recurrent neural network model and its superior convergence when activated by the aforementioned nonlinear activation functions.

Random Neural Networks with Multiple Classes of Signals

1999 ◽  
Vol 11 (4) ◽  
pp. 953-963 ◽  
Author(s):  
Erol Gelenbe ◽  
Jean-Michel Fourneau
Keyword(s):  
Neural Network ◽  
Stationary Solution ◽  
Network Model ◽  
Neural Network Model ◽  
Sufficient Conditions ◽  
Image Texture ◽  
External Signal ◽  
Multiple Signal ◽  
Random Neural Network ◽  
Texture Generation

By extending the pulsed recurrent random neural network (RNN) discussed in Gelenbe (1989, 1990, 1991), we propose a recurrent random neural network model in which each neuron processes several distinctly characterized streams of “signals” or data. The idea that neurons may be able to distinguish between the pulses they receive and use them in a distinct manner is biologically plausible. In engineering applications, the need to process different streams of information simultaneously is commonplace (e.g., in image processing, sensor fusion, or parallel processing systems). In the model we propose, each distinct stream is a class of signals in the form of spikes. Signals may arrive to a neuron from either the outside world (exogenous signals) or other neurons (endogenous signals). As a function of the signals it has received, a neuron can fire and then send signals of some class to another neuron or to the outside world. We show that the multiple signal class random model with exponential interfiring times, Poisson external signal arrivals, and Markovian signal movements between neurons has product form; this implies that the distribution of its state (i.e., the probability that each neuron of the network is excited) can be computed simply from the solution of a system of 2Cn simultaneous nonlinear equations where C is the number of signal classes and n is the number of neurons. Here we derive the stationary solution for the multiple class model and establish necessary and sufficient conditions for the existence of the stationary solution. The recurrent random neural network model with multiple classes has already been successfully applied to image texture generation (Atalay & Gelenbe, 1992), where multiple signal classes are used to model different colors in the image.

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