Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

Svetoslav G. Nikolov and Vassil M. Vassilev
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Svetoslav G. Nikolov: Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, Bulgaria
Vassil M. Vassilev: Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, Bulgaria

Mathematics, 2021, vol. 9, issue 18, 1-14

Abstract: In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.

Keywords: analysis; synchronization; nonlinear dynamics; Hopf–Langford system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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