A computer-assisted proof for the existence of horseshoe in a novel chaotic system

Topological horseshoe analysis and the circuit implementation for a four-wing chaotic attractor

“…In order to explain the m-shift map, we first recall some aspects of symbolic dynamics [12,14,15,17]. …”

“…With the distance defined as in (2), X is a metric space, and the following facts are well known Theorem 2 [12,14,15,17] The space X is…”

“…For example, Yang et al prove the existence of a horseshoe in a foodwed model [12], in modified Chen's attractors [13], in the Rossler [14], in Josephson junction [15], in a class of simple Hopfield neural networks [16], respectively. Wu et al also prove the existence of a horseshoe in a novel chaotic system [17]. Therefore, it can be an interesting work to prove the existence of a horseshoe in some reported chaos by the computer-assisted method.…”

Chaos and rigorous verification of horseshoes in a class of Hopfield neural networks

“…Many efforts have been made on applying neural networks to various fields. Retrieving and creation of information in neural networks have also received considerable attentions in the recent years [3][4][5][6][7][8][9][10][11]. Lately, chaos was numerically observed in three-dimensional continuous time neural networks and has been investigated in several papers [12][13][14][15][16].…”

“…The subsets a 1 , a 2 and the image of a 1 with the connection matrix (6); b The subsets a 1 , a 2 and the image of a 2 with the connection matrix(6) …”