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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-24 23:02 |
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Conference: Bucharest University Faculty of Physics 2015 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
Prediction tools in nonlinear dynamics
Authors:
Noel-Mircea ZUS (1,2), Virgil BARAN (1)
Affiliation:
1)Faculty of Physics, University of Bucharest
2)Constanta Maritime University
E-mail
zusmircea@gmail.com
Keywords:
nonlinear dynamics, complex systems, Lyapunov exponent, chaotic dynamics
Abstract:
The ability to predict the appearance of chaotic dynamics when dealing with nonlinear systems is a characteristic feature necessary in the study of certain phenomena. There has been a necessity to study some suitable quantities that characterize the conditions for a nonlinear system, dissipative or conservative, to display chaotic dynamics. We study the behavior of d∞ in simple one-dimensional maps. We study the asymptotic distance between trajectories d∞ in order to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponent, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. Near a critical point, d∞ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponent, it shows jumps when there are sudden changes on the available phase-space.
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