Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System. (30th March 2014)

• Record Type: Journal Article
• Authors: Liu, Qingsong; Lin, Yiping; Cao, Jingnan; Cao, Jinde
• Other Names: Yu Wenwu Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-03-30
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/139375
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing τ as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.