Boundedness and Stability for Integrodifferential Equations Modeling Neural Field with Time Delay

Authors:
Xuyang Lou;Baotong Cui
Affiliations:
louxuyang28945@163.com;Research Center of Control Science and Engineering, Southern Yangtze University, Wuxi, Jiangsu 214122, P.R.C., btcui@vip.sohu.com
Venue:
Neural Computation
Year:
2007

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Abstract

In this letter, delayed integrodifferential equations modeling neural field (DIEMNF) is studied. The model of DIEMNF is first established as a modified neural field model. Second, it has been proved that if the interconnection of neural field is symmetric, then every trajectory of the system converges to an equilibrium. The boundedness condition for integrodifferential equations modeling neural field with delay is obtained. Moreover, when the interconnection is asymmetric, we give a sufficient condition that can guarantee that the equilibrium of the DIEMNF is unique and is also a global attractor.