Chen Yuanlong, Huang Tingwen, Huang Yu
Mathematics Department, GuangDong University of Finance, Guangzhou 510521, People's Republic of China.
Mathematics Department, Texas A&M University at Qatar, P. O. Box 23874, Doha, Qatar.
Chaos. 2014 Mar;24(1):013108. doi: 10.1063/1.4861756.
In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.
