Invariant set based distributed protocol for synchronization of discrete-time heterogeneous systems with nonlinear dynamics

2020 ◽  
Vol 102 ◽  
pp. 56-67
Author(s):  
Zhikun She ◽  
Qiqi Hao ◽  
Quanyi Liang ◽  
Lei Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Discrete Time ◽  
Heterogeneous Systems ◽  
Invariant Set ◽  
Distributed Protocol

scholarly journals Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Min Wan ◽  
Jianping Gou ◽  
Desong Wang ◽  
Xiaoming Wang
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Firing Rate ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Invariant Set ◽  
Bifurcation And Chaos ◽  
Dynamical Properties ◽  
Background Input

The dynamics of a discrete-time background network with uniform firing rate and background input is investigated. The conditions for stability are firstly derived. An invariant set is then obtained so that the nondivergence of the network can be guaranteed. In the invariant set, it is proved that all trajectories of the network starting from any nonnegative value will converge to a fixed point under some conditions. In addition, bifurcation and chaos are discussed. It is shown that the network can engender bifurcation and chaos with the increase of background input. The computations of Lyapunov exponents confirm the chaotic behaviors.

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