Chaotic behavior of modified stretch-twist-fold (STF) flow with fractal property

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

The Tangled Tale of Phase Space

10.1093/oso/9780198805847.003.0006 ◽

2018 ◽

Author(s):

David D. Nolte

Keyword(s):

Phase Space ◽

Chaotic Behavior ◽

Three Body Problem ◽

Henri Poincaré ◽

History Of ◽

The Stability ◽

Three Body ◽

Space Phase ◽

Central Paradigm ◽

System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501979 ◽

2019 ◽

Vol 29 (14) ◽

pp. 1950197 ◽

Cited By ~ 2

Author(s):

P. D. Kamdem Kuate ◽

Qiang Lai ◽

Hilaire Fotsin

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Lorenz System ◽

Chaotic Behavior ◽

Piecewise Linear ◽

Period Doubling ◽

Adaptive Synchronization ◽

The Novel ◽

Algebraic Equations ◽

The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Qualitative Properties of Autocatalytic Reactions Occurring in a Flow System

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0715 ◽

1985 ◽

Vol 40 (7) ◽

pp. 736-747

Author(s):

Sang H. Kim ◽

Vladimir Hlavacek

Keyword(s):

Chaotic Behavior ◽

Flow System ◽

Cell Model ◽

Dispersion Model ◽

Travelling Waves ◽

Continuous Model ◽

Product Inhibition ◽

Stable Node ◽

Qualitative Properties ◽

Intermediate Value

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

Chaotic behavior of a stack of intrinsic Josephson junctions at the transition to branching for overcritical currents

Chinese Journal of Physics ◽

10.1016/j.cjph.2021.03.025 ◽

2021 ◽

Vol 71 ◽

pp. 634-642

Author(s):

Marina Cuzminschi ◽

Alexei Zubarev

Keyword(s):

Josephson Junctions ◽

Chaotic Behavior ◽

Intrinsic Josephson Junctions

On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation

Engineering With Computers ◽

10.1007/s00366-020-01210-9 ◽

2021 ◽

Author(s):

Lianghua Ma ◽

Xiaoliang Liu ◽

Zohre Moradi

Keyword(s):

Chaotic Behavior ◽

Harmonic Excitation

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

Modern Physics Letters B ◽

10.1142/s0217984989001813 ◽

1989 ◽

Vol 03 (15) ◽

pp. 1185-1188 ◽

Cited By ~ 1

Author(s):

J. SEIMENIS

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Infinite Number ◽

Chaotic Behavior ◽

Equations Of Motion ◽

Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.