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The study of Newton–Raphson basins of convergence in the three-dipole problem
- Source :
- Nonlinear Dynamics. 107:829-854
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We consider a system in which the charged particle orbits under the influence of the electromagnetic field of three dipoles located on a system of three celestial bodies. Using well-known bivariate iterative scheme, known as Newton–Raphson (NR) iterative scheme, we numerically evaluated the positions of the stationary points (SPs) or equilibrium points (EPs) or libration points (LPs) and the linked basins of convergence (BoCs), and we also evaluated their linear stability. Moreover, we unveiled how the parameters, entering the effective potential function, affect the convergence dynamics of the system. Moreover, we also unveiled how the involved parameters affect the geometry of the zero velocity curves (ZVCs). Further, the correlation with the required number of iterations and the regions of convergence as well as the probability distributions associated to the BoCs is illustrated. In order to quantify the degree of final-state uncertainty of the BoCs, the basin entropy (BE) and for the fractality of boundaries of BoCs, the boundary basin entropy (BBE) are computed.
- Subjects :
- Entropy (statistical thermodynamics)
Applied Mathematics
Mechanical Engineering
Mathematical analysis
Aerospace Engineering
Lagrangian point
Boundary (topology)
Ocean Engineering
Stationary point
symbols.namesake
Control and Systems Engineering
Convergence (routing)
symbols
Probability distribution
Electrical and Electronic Engineering
Newton's method
Linear stability
Mathematics
Subjects
Details
- ISSN :
- 1573269X and 0924090X
- Volume :
- 107
- Database :
- OpenAIRE
- Journal :
- Nonlinear Dynamics
- Accession number :
- edsair.doi...........123f40082d40a33528f722aefe384216