Open AccessJacobi stability analysis and impulsive control of a 5D self-exciting homopolar disc dynamo
Author(s) -
Zhouchao Wei,
Fanrui Wang,
Huijuan Li,
Wei Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021263
Subject(s) - homopolar motor , dynamo , attractor , stability (learning theory) , instability , mathematics , dynamo theory , mathematical analysis , counterexample , lyapunov exponent , physics , control theory (sociology) , classical mechanics , computer science , mechanics , control (management) , magnetic field , nonlinear system , quantum mechanics , artificial intelligence , discrete mathematics , machine learning , magnet
In this paper, we make a thorough inquiry about the Jacobi stability of 5D self-exciting homopolar disc dynamo system on the basis of differential geometric methods namely Kosambi-Cartan-Chern theory. The Jacobi stability of the equilibria under specific parameter values are discussed through the characteristic value of the matrix of second KCC invariants. Periodic orbit is proved to be Jacobi unstable. Then we make use of the deviation vector to analyze the trajectories behaviors in the neighborhood of the equilibria. Instability exponent is applicable for predicting the onset of chaos quantitatively. In addition, we also consider impulsive control problem and suppress hidden attractor effectively in the 5D self-exciting homopolar disc dynamo.