Hopf Bifurcation, Multistability and its Control in a Satellite System

Tchinda, T. H.; Wouapi, K. Marcel; Njitacke, Zeric Tabekoueng; Fozin, T. Fonzin; Gninzanlong, Carlos Lawrence; Fotsin, Hilaire Bertrand

doi:10.1007/s42417-022-00567-z

Cited by 1 publication

(1 citation statement)

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“…The aim of studying the chaotic nonlinear dynamics of jerk systems is to understand the complex behavior that arises in systems that exhibit sudden changes in acceleration [9]. Aside from jerk systems themselves, the study of such nonlinear systems can reveal information on the behavior of physical systems such as earthquakes [10,11], satellites [12,13], and biological systems [14][15][16]. The chaotic behavior of jerk systems can also be applied in engineering applications such as control systems, robotics, and signal processing [17,18].…”

Section: Introductionmentioning

confidence: 99%

Energy function and complex dynamics from a jerk system

Yu,

Njitacke,

Jiang

et al. 2023

Phys. Scr.

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Jerk, as a mathematical concept, is used in mechanics to describe the rate of change of acceleration and plays a crucial role in the design of control systems for machines and vehicles. Therefore, it is important to master the various states and the energy released during the change of acceleration. This is why a new simple jerk function introduced afterward, energy released, is derived from a Hamilton function using the Helmholtz theorem. The condition of having a stable or unstable rate of change of acceleration is established using Hopf bifurcation theory. Some two-parameter stability charts are then computed for a suitable selection region of the study. Using some nonlinear analysis metrics, in the unstable region of the study, the occurrence of phenomena is found, such as reverse period doubling bifurcation, antimonotonicity, and hysteresis involving the coexistence of the states in the considered jerk system. An electronic circuit is built and used to implement the mathematical expression of the jerk equation and validate the result of the theoretical investigation.

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