1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model. (17th December 2014)

• Record Type: Journal Article
• Authors: Li, Bo; He, Zhimin
• Other Names: Teng Zhidong Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-12-17
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/896478
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 1 : 3 resonance of a two-dimensional discrete Hindmarsh-Rose model is discussed by normal form method and bifurcation theory. Numerical simulations are presented to illustrate the theoretical analysis, which predict the occurrence of a closed invariant circle, period-three saddle cycle, and homoclinic structure. Furthermore, it also displays the complex dynamical behaviors, especially the transitions between three main dynamical behaviors, namely, quiescence, spiking, and bursting.