Please use this identifier to cite or link to this item: http://hdl.handle.net/2080/4652
Title: Analysis of Butterfly Effect using Nambu Formalism
Authors: Patra, Tanmayee
Ganguli, Biplab
Keywords: Chaotic dynamics
Butterfly effect
Strange attractors
Lyapunov characteristic exponent(LE)
Nambu mechanics
Nambu doublets
Intersecting orbits
Euler-top deformation
Issue Date: Jul-2024
Citation: International Conference on 60 Years of DFT: Advancements in Theory & Computation, IIT Mandi, India, 21-26 July 2024
Abstract: Nonlinear dynamics is at the heart of the modern interdisciplinary approach to science. In this article, chaotic Fourwing attractor is investigated by means of some of the diagnostic tools such as bifurcation diagram, Lyapunov characteristic exponents, Poincar´e maps to measure the extent of chaos . Here, a 3-dimensional autonomous chaotic Fourwing attractor is analyzed with the help of phase-space geometry using Nambu mechanics. From geometrical point of view, it is observed that with the help of Nambu mechanics the non-dissipative part of the chaotic system can be generated by the intersection of two quadratic surfaces that form a Nambu doublet. All manifolds are classified into four distinct classes; parabolic, hyperbolic, cylindrical and elliptical. By using different linear transformations with Jacobian J=1, we can find different classes of doublets associated with the chaotic system. The boundaries of the attractor is also found. Another interesting fact we find that this Nambu mechanics framework can be extended to include dissipation in R3 phase-space. We demonstrate that the dissipative Nambu dynamics give rise to the intersecting surfaces of the strange attractor in a very intuitive manner accounting their gross topological aspects.
Description: Copyright belongs to proceeding publisher
URI: http://hdl.handle.net/2080/4652
Appears in Collections:Conference Papers

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