arXiv subjects

Nikolay K. Vitanov

Publications and source records attributed to Nikolay K. Vitanov.

47 records · Page 3Linked to original sources

arXiv2012

Discrete Model of Ideological Struggle Accounting for Migration

A discrete in time model of ideological competition is formulated taking into account population migration. The model is based on interactions between global populations of non-believers and followers of different ideologies. The complex dynamics of the attracting manifolds is investigated. Conversion from one ideology to another by means of (i) mass media influence and (ii) interpersonal relations is considered. Moreover a different birth rate is assumed for different ideologies, the rate being assumed to be positive for the reference population, made of initially non-believers. Ideological competition can happen in one or several regions in space. In the latter case, migration of non-believers and adepts is allowed; this leads to an enrichment of the ideological dynamics. Finally, the current ideological situation in the Arab countries and China is commented upon from the point of view of the presently developed mathematical model. The massive forced conversion by Ottoman Turks in the Balkans is briefly discussed.

physics.soc-ph↗

arXiv2012

Knowledge epidemics and population dynamics models for describing idea diffusion

The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for improved welfare and economic growth is briefly described from a historical point of view. Next, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through (i) deterministic, (ii) stochastic, and (iii) statistical approaches. These are illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations. The deterministic dynamical models are considered to be appropriate for analyzing the evolution of large and small societal, scientific and technological systems when the influence of fluctuations is insignificant. Stochastic models are appropriate when the system of interest is small but when the fluctuations become significant for its evolution. Finally statistical approaches and models based on the laws and distributions of Lotka, Bradford, Yule, Zipf-Mandelbrot, and others, provide much useful information for the analysis of the evolution of systems in which development is closely connected to the process of idea diffusion.

physics.soc-ph↗

arXiv2011

Verhulst-Lotka-Volterra (VLV) model of ideological struggles

Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds of influences can be used, in such a model, for describing the dynamics of an agent opinion conversion: this can occur (i) either by means of mass communication tools, under some external field influence, or (ii) by means of direct interactions between agents. It results, among other features, that change(s) in environmental conditions can prevent the extinction of populations of followers of some ideology due to different kinds of resurrection effects. The tension arising in the country population is proposed to be measured by an appropriately defined scale index.

physics.soc-ph↗

arXiv2009

A model of ideological struggle

A general model for opinion formation and competition, like in ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. Several ideologies compete to increase their number of adepts. Such followers can be either converted from one ideology to another or become followers of an ideology though being previously ideologically-free. A reverse process is also allowed. We consider two kinds of conversion: unitary conversion, e.g. by means of mass communication tools, or binary conversion, e.g. by means of interactions between people. It is found that the steady state,when it exists, depends on the number of ideologies. Moreover when the number of ideologies increases some tension arises between them. This tension can change in the course of time. We propose to measure the ideology tensions through an appropriately defined scale index.

physics.soc-ph↗

arXiv2008

Generalization of the model of conflict between two armed groups

The conflicts between armed groups often go on for years. The classical model of such conflicts accounts for the number of participants and for the technology level of the equipment of the groups. Below we extend this model in order to account for events that are present for limited time. As examples we discuss three kinds of such events: inclusion of reserves, presence of epidemics and use of non-conventional weapons. We show that if such events are not handled properly by the leaders of the groups the corresponding group can lose the conflict.

physics.soc-ph↗

arXiv2008

Mathematical models of intergroup conflicts

The human society today is far from perfection and conflicts between groups of humans are frequent events. One example for such conflicts are armed intergroup conflicts. The collective behavior of the large number of cooperating participants in these conflicts allows us to describe the conflict on the basis of models containing only few variables. In this paper we discuss several cases of conflicts without use of weapons of non-conventional kind. In the ancient times the Chinese writer Sun Tsu mentioned that the war is an art. We can confirm that the conflict is an art but with much mathematics at the background.

physics.soc-ph↗

arXiv2006

Hoelder-exponent-MFDFA-based test for long-range correlations in pseudorandom sequences

We discuss the problem for detecting long-range correlations in sequences of values obtained by generators of pseudo-random numbers. The basic idea is that the H{ö}lder exponent for a sufficiently long sequence of uncorrelated random numbers has the fixed value $h=1/2$. The presence of long-range correlations leads to deviation from this value. We calculate the H{ö}lder exponent by the method of multifractal detrended fluctuation analysis (MFDFA). We discuss frequently used tests for randomness, finite sample properties of the MFDFA, and the conditions for a correct application of the method. We observe that the fluctuation function $F_{q}$ used in the MFDFA reacts to trends caused by low periodicity presented in the pseudo-random number generator. In order to select appropriate generators from the numerous programs we propose a test for the ensemble properties of the generated pseudo-random sequences with respect to their robustness against presence of long-range correlations, and a selection rule which orders the generators that pass the test. Selecting generators that successfully pass the ensemble test and have good performance with respect to the selection rule is not enough. For the selected generator we have to choose appropriate pseudo-random sequences for the length of the sequence required by the solved problem. This choice is based on the closeness of the H{ö}lder exponent of the generated sequence to its value 1/2 characteristic for the case of absence of correlations.

physics.data-an↗

arXiv2006

Analysis of a Japan government intervention on the domestic agriculture market

We investigate an economic system in which one large agent - the Japan government changes the environment of numerous smaller agents - the Japan agriculture producers by indirect regulation of prices of agriculture goods. The reason for this intervention was that before the oil crisis in 1974 Japan agriculture production prices exhibited irregular and large amplitude changes. By means of analysis of correlations and a combination of singular spectrum analysis (SSA), principal component analysis (PCA), and time delay phase space construction (TDPSC) we study the influence of the government measures on the domestic piglet prices and production in Japan. We show that the government regulation politics was successful and leaded (i) to a decrease of the nonstationarities and to increase of predictability of the piglet price; (ii) to a coupling of the price and production cycles; (iii) to increase of determinism of the dynamics of the fluctuations of piglet price around the year average price. The investigated case is an example confirming the thesis that a large agent can change in a significant way the environment of the small agents in complex (economic or financial) systems which can be crucial for their survival or extinction.

physics.soc-ph↗

arXiv2005

Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster

Time series of heartbeat activity of humans can exhibit long-range correlations. In this paper we show that such kind of correlations can exist for the heartbeat activity of much simpler species like Drosophila melanogaster. By means of the method of multifractal detrended fluctuation analysis (MFDFA) we calculate fractal spectra $f(α)$ and $h(q)$ and investigate the correlation properties of heartbeat activity of Drosophila with genetic hearth defects for three consequent generations of species. We observe that opposite to the case of humans the time series of the heartbeat activity of healtly Drosophila do not have scaling properties. Time series from flies with genetic defects can be long-range correllated and can have multifractal properties. The fractal heartbeat dynamics of Drosophila is transferred from generation to generation.

physics.data-an↗

arXiv2005

On correlations and fractal characteristics of time series

Correlation analysis is convenient and frequently used tool for investigation of time series from complex systems. Recently new methods such as the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maximum method (WTMM) have been developed. By means of these methods (i) we can investigate long-range correlations in time series and (ii) we can calculate fractal spectra of these time series. But opposite to the classical tool for correlation analysis - the autocorrelation function, the newly developed tools are not applicable to all kinds of time series. The unappropriate application of MFDFA or WTMM leads to wrong results and conclusions. In this article we discuss the opportunities and risks connected to the application of the MFDFA method to time series from a random number generator and to experimentally measured time series (i) for accelerations of an agricultural tractor and (ii) for the heartbeat activity of {\sl Drosophila melanogaster}. Our main goal is to emphasize on what can be done and what can not be done by the MFDFA as tool for investigation of time series.

physics.data-an↗

arXiv2004

Dynamical Properties of nystagmus

By the methods of the time series analysis we investigate human vestibular and optovestibular nystagmus time series. They can be stationary or nonstationary and are between the classes of purely periodic or purely chaotic time series. The amplitudes of the autocorrelation functions of the time series have an unexpected peak between 7 and 9 seconds on the time axis. The singular spectrum analysis shows that the important information about the time series is concentrated in the first four to six principal components. The influence of the sensory input modality, which can be changed by opening or closing eyes of the investigated persons, leads to changes in the histogram, but leaves almost unchanged other important characteristics of the time series such as the statistical dimension or the positions of the dominant frequencies in the power spectrum. Thus the behavior of the studied time series shows a presence of nonlinearities which could play an important role for realization of the nystagmus phenomenon.

nlin.CD↗