Abstract
A continuous attractor of a recurrent neural network is a set of connected stable equilibrium points. The continuous attractors of neural networks with symmetric connection weights have been studied widely. However, most of the matrixes are asymmetric. In this paper, the continuous attractors of 3-D discrete-time ring networks with circulant weight matrix are studied. The circulant matrix is asymmetric. The eigenvalues of asymmetric matrix may be complex. Based on the complex eigenvalues, the conditions that guarantee the networks with circulant weight matrix to have continuous attractors are obtained.
J. Yu—This work is supported by National Natural Science Foundation of China under Grant 61572112, 61103041, 61432012, the Fundamental Research Funds for the Central Universities under Grant ZYGX2016J136.
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Yu, J., Yi, Z., Liao, Y., Wu, DA., Dai, X. (2018). Continuous Attractors of 3-D Discrete-Time Ring Networks with Circulant Weight Matrix. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_45
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