Chaos by Neural Networks

2016-01-01
Akhmet, Marat
Fen, Mehmet Onur
REPLICATION OF CHAOS IN NEURAL NETWORKS, ECONOMICS AND PHYSICS

Suggestions

Chaos from massive deformations of Yang-Mills matrix models
Başkan, K.; Kürkcüoğlu, Seçkin; Oktay, O.; Taşcı, Cankut (Springer Science and Business Media LLC, 2020-10-01)
We focus on an SU(N) Yang-Mills gauge theory in 0 + 1-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global SO(9) symmetry of the latter to SO(5) x SO(3) x Z(2). Introducing an ansatz configuration involving fuzzy four and two spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels N = ...
Chaos in Yang-Mills matrix models
Başkan, Kağa; Kürkcüoğlu, Seçkin; Department of Physics (2019)
In this thesis, chaotic dynamics emerging from Yang-Mills matrix models are investigated. Firstly, we investigate the Yang-Mills two-matrix models with ChernSimons term using both analytical and numerical methods. In particular, we obtain the Poincaré sections and Lyapunov exponents at several different values of the parameters of the model, revealing the detailed structure of the chaotic dynamics. In the second part of the thesis, we focus on a massive deformation of the bosonic part of the Banks-Fischler-...
Chaos in Matrix Gauge Theories with Massive Deformations
Başkan, K.; Kürkcüoğlu, Seçkin; Oktay, O.; Taşcı, Cankut (2022-11-23)
Starting from an SU(N) matrix quantum mechanics model with massive deformation terms and by introducing an ansatz configuration involving fuzzy four- and two-spheres with collective time dependence, we obtain a family of effective Hamiltonians, Hn, (N = 16 (n + 1)(n + 2)(n + 3)) and examine their emerging chaotic dynamics. Through numerical work, we model the variation of the largest Lyapunov exponents as a function of the energy and find that they vary either as ∝ (E − (En)F)1/4 or ∝ E1/4, where (En)F stan...
Chaos Generation in Continuous/Discrete-Time Models
Akhmet, Marat; Fen, Mehmet Onur (2016-01-01)
Chaos generation in hyperbolic systems
Akhmet, Marat; FEN, MEHMET ONUR (2012-01-01)
© 2012 L & H Scientific Publishing, LLC.In the present paper, we consider extension of chaos in hyperbolic systems with arbitrary large dimensions. Our investigations comprise chaos in the sense of both Devaney and Li-Yorke. We provide a mechanism for unidirectionally coupled systems through the insertion of chaos from one system to another, where the latter is initially nonchaotic. In our procedure for the chaos extension, we take advantage of chaotic sets of functions to provide mathematically approved re...
Citation Formats
M. Akhmet and M. O. Fen, “Chaos by Neural Networks,” REPLICATION OF CHAOS IN NEURAL NETWORKS, ECONOMICS AND PHYSICS, pp. 311–405, 2016, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99023.