Multistable learning dynamics in second-order neural networks with time-varying delays

Abstract

In this paper, we present new results on multistability and attractivity of second-order networks with unsupervised Hebbian-type learning component and time-varying delays. By using the properties of activation functions, we divide state space into invariant sets and establish new criteria of coexistence of equilibrium points which are exponentially stable. The attained results show that second-order synaptic interactions and learning behaviour have an important effect on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable learning dynamics of second-order networks.

Keywords:

• multistability
• attractivity
• second-order networks
• Hebbian learning
• exponential stability

2000 AMS Subject Classifications :

• 34D20
• 92B20
• 37B25

Acknowledgements

This work is supported by the Foundation of Education of Fujian Province, China (JA07142), the Foundation for Young Professors of Jimei University, the Scientific Research Foundation of Jimei University, the Foundation for Talented Youth with Innovation in Science and Technology of Fujian Province (2009J05009) and the National Natural Science Foundation of China under Grants 10961005.