Homoclinic orbits and Jacobi stability on the orbits of Maxwell–Bloch system. Issue 13 (2nd September 2022)

• Record Type: Journal Article
• Authors: Liu, Yongjian; Chen, Haimei; Lu, Xiaoting; Feng, Chunsheng; Liu, Aimin
• Is Part Of: Applicable analysis. Volume 101:Issue 13(2022)
• Page Start: 4377
• Page End: 4396
• Publication Date: 2022-09-02
• Subjects: Maxwell–Bloch system -- homoclinic orbit -- KCC-theory -- Jacobi stability -- chaos; 34D35 -- 53B40 -- 53C60 -- 37C29; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1854235
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we analytically and geometrically investigate the complexity of Maxwell–Bloch system by giving new insight. In the first place, the existence of homoclinic orbits is rigorously proved by means of the generalized Melnikov method. More precisely, for 6 a −2 b > c and d >0, it is certified analytically that Maxwell–Bloch system has two nontransverse homoclinic orbits. Secondly, Jacobi stability on the orbits of Maxwell–Bloch system is examined in view point of Kosambi–Cartan–Chern theory (KCC-theory). In other words, in the light of the deviation curvature tensor of the five corresponding invariant associated to the reformulated Maxwell–Bloch system, we further proved that Jacobi stability of all equilibria under appropriate parameters. Moreover, the deviation vector, as well as the curvature of the deviation vector near equilibrium points, is focused to interpret the chaotic behavior of Maxwell–Bloch system in Finsler geometry.