Multistability in Networks With Self-Excitation and High-Order Synaptic Connectivity

作者：Huang, Zhenkun^*; Song, Qiankun; Feng, Chunhua

来源：IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2010, 57(8): 2144-2155.

DOI：10.1109/TCSI.2009.2037401

• Division regions
• exponential stability
• high-order synaptic connectivity
• self-excitation

This paper presents new results on multistability of networks when neurons undergo self-excitation and second-order synaptic connectivity. Due to self-excitation of neurons, we split state space into invariant regions and establish new criteria of coexistence of equilibria (periodic orbits) which are exponentially stable. It is shown that high-order synaptic connectivity and external inputs play an important role on the number of equilibria and their convergent dynamics. As a consequence, our results refute traditional viewpoint: high-order interactions of neurons have faster convergence rate and greater storage capacity than first-order ones. Finally, numerical simulations will illustrate our new and interesting results.

• 出版日期2010-8
• 单位集美大学; 重庆交通大学; 广西师范大学