Complex Dynamics of Discrete-Time Ring Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150116
Author(s):  
Xiaoying Wu ◽  
Yuanlong Chen ◽  
Liangliang Li ◽  
Fen Wang
Keyword(s):  
Neural Network ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Delays ◽  
Complex Dynamics ◽  
Multiple Time ◽  
Chaotic Neural Network ◽  
Multiple Time Delays ◽  
Ring Neural Network ◽  
Theoretical Results

This paper mainly considers the complex dynamics of a discrete-time ring neural network with multiple time delays. By transforming the network system into a system of difference equations, one can obtain a chaotic neural network. More specifically, by projection method one can determine a closed invariant set of the system governed by some difference equations, and prove that some invariant subsystem is topologically conjugate to the two-sided symbolic dynamical system. Moreover, numerical simulations are presented to verify the theoretical results.

scholarly journals Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Zhuoyan Gao ◽  
JinRong Wang ◽  
Yong Zhou
Keyword(s):  
Iterative Learning Control ◽  
Time Delays ◽  
Iterative Learning ◽  
Multiple Time ◽  
Weighted Norm ◽  
Differential Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
Two Parameters ◽  
Theoretical Results

We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results.

Bifurcation, Synchronization, and Multistability of Two Interacting Networks with Multiple Time Delays

2016 ◽  
Vol 26 (09) ◽  
pp. 1650156 ◽  
Author(s):  
Xiaochen Mao
Keyword(s):  
Time Delays ◽  
Nearest Neighbor ◽  
Pitchfork Bifurcation ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Trivial Equilibrium ◽  
Dynamical Properties ◽  
Interacting Networks ◽  
Delay Dependent ◽  
Theoretical Results

This paper reveals the dynamical properties of two interacting neural networks with multiple couplings. Different time delays are introduced into the nearest-neighbor links and long-range connections in each layer and the couplings between different substructures. The delay-dependent and delay-independent stability and the oscillations bifurcated from the trivial equilibrium of the network are analyzed. The conditions of the existence of nontrivial equilibria and pitchfork bifurcation are discussed. Numerical simulations are performed to validate the theoretical results and interesting neuronal activities are observed, such as completely synchronous oscillations, three types of asynchronous oscillations, multiple switches between the rest states and different oscillations, coexistence of different oscillations, and coexistence of nontrivial equilibria and oscillations.

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