Bifurcation analysis with chaotic motion of oblique plane wave for describing a discrete nonlinear electrical transmission line with conformable derivative

• Main Authors: Iqbal, S.A., Hafez, M.G., Abdul Karim, S.A.
• Format: Article
• Published: Elsevier B.V. 2020
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089345549&doi=10.1016%2fj.rinp.2020.103309&partnerID=40&md5=1d5433e03d109423c86d4e9e7804d5d6; http://eprints.utp.edu.my/30029/

The present work discusses the basic features of bifurcation properties with chaotic motion of oblique plane wave in the discrete nonlinear electrical transmission lines having conformable derivative evolution. The planar dynamical systems are obtained to understand such physical issues for this model. In addition, the analytical plane wave solutions of nonlinear mathematical leading equation are determined by using two different mathematical methods. Both methods are supported only by the shock plane wave solutions. The conditions for other types of oscillatory plane wave solutions are also determined. The effect of obliqueness on the bifurcation properties, chaotic motion and shock plane waves structures are focused graphically with discussions by considering both of locality and non-locality in the system. It is found that the parameter of non-local operator is only affected on the nonlinear shock wave phenomena, whereas all basic features of discrete nonlinear electrical transmission line are changed with the changes of obliqueness. © 2020 The Author(s)