TY - JOUR
T1 - Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Unbounded Time-Varying Delays
AU - Liu, Peng
AU - Zeng, Zhigang
AU - Wang, Jun
PY - 2018/7
Y1 - 2018/7
N2 - This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an n-neuron neural network can exhibit ∏ni=1(2Ki + 1) equilibrium points with Ki ≥ 0. In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of ∏ni=1(Ki + 1) equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.
AB - This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an n-neuron neural network can exhibit ∏ni=1(2Ki + 1) equilibrium points with Ki ≥ 0. In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of ∏ni=1(Ki + 1) equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.
KW - Asymptotic stability
KW - Biological neural networks
KW - Delay effects
KW - Delays
KW - Learning systems
KW - Multistability
KW - nonmonotonic activation functions
KW - recurrent neural networks
KW - unbounded time-varying delays.
UR - http://www.scopus.com/inward/record.url?scp=85023781211&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85023781211&origin=recordpage
U2 - 10.1109/TNNLS.2017.2710299
DO - 10.1109/TNNLS.2017.2710299
M3 - RGC 21 - Publication in refereed journal
SN - 2162-237X
VL - 29
SP - 3000
EP - 3010
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 7
ER -