## Simple Chaotic systems and Jerky Systems of physical interest

**Avadis Hacınlıyan**

*Yeditepe University, Istanbul*

12 May 2016, Thursday, 14:40

Cavid Erginsoy Seminar Room, Physics Department, 3rd floor

**Abstract:**
In this work simple three variable non Hamiltonian chaotic systems studied by Sprott[1] and four variable Hamiltonian systems [2] derived from truncations of cyclically interacting three body next neighbor (Toda) systems will be introduced because of the recent physical interest generated by their application. Their transition to chaotic behavior, dynamical invariants and their attractors will be analyzed.
The simple three variable chaotic systems with resonant characteristics and possible candidates for demonstrating Hopf Bifurcation will be emphasized. The derivation of jerky dynamical systems has also become of interest. Occasionally, the jerky systems involve discontinuous functions and calculation of dynamical invariants require approximation of these by two different continuous functions.[3] Chaotic invariants such as Lyapunov exponents and fractal dimensions will be studied. These invariants will be compared between the regular systems and the corresponding derived jerky systems.
The Toda lattice is exactly integrable but its truncations (except for the second order) all show chaotic behavior. Some of these truncations have been of interest in deriving semi classical solutions to gauge theories as demonstrated by Matinyan[4] et.al and results on their chaotic invariants and attractors[5] will be presented.

**References:**

[1] J. C. Sprott, "Some simple chaotic jerk functions" , Am. J. Phys. 65 (6), 537-543 (1997)

[2] İ. Birol, A. Hacinliyan, "A Study on the Possibly Conserved Quantity of the Henon-Heiles problem", Phys. Rev. E 52, (5), .4750-4754 (1995).

[3] A. Hacinliyan, E. Kandiran, "Smoothing discontinuities in Predator Prey Models" 8th CHAOS Conference Proceedings, pp. 357-366, 26-29 May 2015, Henri Poincaré Institute, Paris France

[4] T. S. Biro, S. G. Matinyan, B. Müller, "Chaos and Gauge Field Theory"World Scientific Lecture Notes in Physics, Vol. 56, ISBN 981-02-2079-0, Durham, NC (1994).

[5] O. Özgür Aybar, Avadis S. Hacınlıyan, İlknur Kuşbeyzi Aybar, Kamer Köseyan, Berc Deruni, “Stability and Chaos in a Classical Yang – Mills - Higgs System”, Chaotic Modeling and Simulation (CMSIM) 1: pp. 215-221, (2013).

**Reminder:** Tea and cookies will be in the seminar room before the seminar.