New treatment on bifurcations of periodic and homoclinic orbits in some chaotic systems

Jianghong Bao and Zhongjian Zeng

Chaos, Solitons & Fractals, 2026, vol. 208, issue P1

Abstract: The paper investigates the bifurcations of homoclinic orbits and two types of periodic orbits in four systems, including the Glukhovsky–Dolzhansky model, the Rikitake system, the stretch-twist-fold flow, and the Sprott B system. The four systems are converted into perturbed Hamiltonian systems by choosing an appropriate transformation. By the generalized Melnikov method, the paper analytically proves the existence of two homoclinic orbits in every system. It also explores the existence of two types of periodic orbits and discusses their stability.

Keywords: Homoclinic orbit; Periodic orbit; Bifurcation; Melnikov method; Hamiltonian system (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002973

DOI: 10.1016/j.chaos.2026.118156

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