Homoclinical Structure of Retarded SICNNs with Rectangular Input Currents

Abstract

Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic motions are provided in the functional sense for the multidimensional dynamics of SICNNs, and it is demonstrated that the networks under investigation exhibit such motions. Homoclinic and heteroclinic outputs that are asymptotic to quasi-periodic outputs are illustrated.

Replication of period-doubling route to chaos in impulsive systems

“…([46,47]) Suppose that 𝜇 ∈ [0,4], 𝜏 0 ∈ ℝ, and 𝑑 0 𝜇 ∈ [0, 1] are fixed. A function 𝜙: 𝜏 0 , ∞ → ℝ 3 is called a solution of system(7) if:…”