# Loukas ZachilasUniversity of Thessaly | UTH · Τμήμα Οικονομικών Επιστημών

Loukas Zachilas

Assistant Professor

## About

24

Publications

4,673

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449

Citations

Introduction

Additional affiliations

September 1995 - present

September 1991 - present

## Publications

Publications (24)

In this paper we present a new non–linear, discrete, dynamical system trying to model the historic battle of Salamis (480 BC) between Greeks and Persians. The model describes the most effective strategic behavior between two participants during a battle or in a war. Moreover, we compare the results of the dynamical analysis to Game Theory, consider...

In this paper, we present an innovative non-linear discrete system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle, which took place in late September 480 B.C. The suggested model describes very well the most effective...

Research background: The application of non-linear analysis and chaos theory modelling on financial time series in the discipline of Econophysics.
Purpose of the article: The main aim of the article is to identify the deterministic chaotic behavior of stock prices with reference to Amazon using daily data from Nasdaq-100.
Methods: The paper uses...

The original version of the Zürich sunspot number (Sunspot Number Version 1.0) has been revised by an entirely new series (Sunspot Number Version 2.0). We re-evaluate the performance of our previously proposed models for predicting solar activity in the light of the revised data. We perform new monthly and yearly predictions using the Sunspot Numbe...

In this paper we study a prey–predator dynamical system suitable for species having no overlap between successive generations. Assuming that population evolves in discrete-time steps we investigate the prey refuge effect on prey–predator interactions. Stability analysis is applied in order to investigate the local stability properties of the fixed...

We analyze the yearly mean sunspot-number data covering the period 1700 to 2012. We show that the yearly sunspot number is a low-dimensional deterministic chaotic system. We perform future predictions trying to forecast the solar activity during the next five years (2013 - 2017). We provide evidence that the yearly sunspot-number data can be used f...

We analyze the monthly sunspot number (SSN) data from January 1749 to June 2013. We use the Average Mutual Information
and the False Nearest Neighbors methods to estimate the suitable embedding parameters. We calculate the
correlation dimension to compute the dimension of the system’s attractor. The convergence of the correlation dimension
to its t...

A prey-predator discrete-time model with a Holling type I functional response is investigated by incorporating a prey refuge. It is shown that a refuge does not always stabilize prey-predator interactions. A prey refuge in some cases produces even more chaotic, random-like dynamics than without a refuge and prey population outbreaks appear. Stabili...

In the present paper we study the complex dynamics of non-linear cobweb models of real estate markets in discrete time. Our model incorporates two submarkets, land and housing, interacting with each other. We start by outlining the basic model, which assumes that land prices determine housing supply. This provides the foundations for the developmen...

We study the dynamics in the neighborhood of fixed points in a 4D symplectic
map by means of the color and rotation method. We compare the results with the
corresponding cases encountered in galactic type potentials and we find that
they are in good agreement. The fact that the 4D phase space close to fixed
points is similar to the 4D representatio...

We perform the stability analysis and we study the chaotic behavior of dynamical
systems, which depict the 3-particle Toda lattice truncations through the lens
of the 0-1 test, proposed by Gottwald and Melbourne. We prove that the new test
applies successfully and with good accuracy in most of the cases we
investigated. We perform some comparisons...

Our target in this paper is to observe how the presence of nonlinear terms in the supply and demand model changes the price behavior of the system. The dynamical analysis refers, mainly, to discrete dynamical systems. We start with a simple linear supply and demand model with two markets interacting with each other. The stability conditions for the...

We complete the study of the numerical behavior of the truncated 3-particle Toda lattice (3pTL) with even truncations at orders n=2k, k=2,⋯,10. We use (as in Part I [ibid. No. 10, 3007–3064 (2010; Zbl 1204.37061)]): (a) the method of Poincaré surface of section; (b) the maximum Lyapunov characteristic number; and (c) the ratio of the families of or...

The numerical behavior of the truncated 3-particle Toda lattice (3pTL) is reviewed and studied in more detail (than in previous papers) and at higher energies (at odd-orders n≤9). We further extend our study to higher truncations at odd-orders n=2k+1, k=1,⋯,9. We locate the majority of the families of periodic orbits along with their main bifurcati...

In order to study the structure of the phase space in galactic potentials of three degrees of freedom, we visualize a 4D space of section of the 6D phase space in a 3D Hamiltonian system. The method used is the method of color and rotation [9]. We apply this method to some cases of families of simple periodic orbits in a 3D potential, which describ...

The Society for Space and Astronomy was founded in Volos, Greece, in
1992 and now has more than 500 members, both in Greece and abroad.
Approximately one third of its members are high school students.

The problems encountered in the study of three-dimensional Hamiltonian systems by means of the Poincare cross-sections are reviewed. A new method to overcome these problems is proposed. In order to visualize the four-dimensional “space” of section we introduce the use of color and rotation. We apply this method to the case of a family of simple per...

The problems encountered in the study of 3-dimensional Hamiltonian systems by means of the Poincare cross-sections are reviewed. A new method to overcome these problems is proposed. In order to visualize the four-dimensional "space" of section it is introduced the use of color and rotation. We apply this method to the case of a family of simple per...

An empirical method that uses colors and rotation of 3D figures is proposed for visualizing the 4D “Poincaré space of section” in 3D Hamiltonian systems. The representation of the 4th dimension as color variation in 3D projections, gives essential information about the areas that are close to each other in the 4D space. This method helps us to reve...

An evaluation of the performance of a molecular potential energy function in dynamical calculations can be obtained by constructing bifurcation diagrams of periodic orbits. This is demonstrated for the HCN molecule by using two analytical potential functions which give a global and a local representation of the surface respectively.

It is believed that, in nonintegrable 3D Hamiltonian systems and 4D
mappings, complex instability plays a significant role in introducing
chaos. This paper investigates the rules that may govern complex
instability as the parameters of Hamiltonian (-or mapping) vary
continuously. Various classes of behavior of the complex unstable
regions as the va...

A phase space structure analysis is presented for the van der Waals molecule COAr, based on locating families of periodic orbits. It is found that the classical phase space is predominantly chaotic, even at the zero point energy. Thus most of the bound quantum eigenfunctions are delocalized, except for a few of them, which show characteristic loca...

This paper examines the role that complex instability of simple periodic
orbits plays in the dynamics of a realistic two-component galactic
model. The main families of simple periodic orbits which have large
complex unstable regions and their bifurcations are identified, with
particular attention given to bifurcations that arise from the y-axis
fam...

## Projects

Project (1)