Belousov-Zhabotinsky reaction 1 is a chemical reaction, or more precisely a reaction family, known for exhibiting temporal and spatial oscillations.
This reaction is one of the classical examples of the natural non-linear oscillations. Another prominent example is the previously analyzed prey-predator interactions in the ecosystem. Interestingly enough despite being of a very different nature both of these example can be modeled using Lotka-Volterra equations.
Previously we wrote about mathematical “puzzle” originating from a TV game (see the description of the Monty Hall problem). This time we shall consider the opposite case – the mathematical “game” used as a base for a TV game. Watch a fragment of the “Golden Balls” final stage called “Split or steal”.
The game is very simple, yet it possesses no correct solution or optimal strategy. Interestingly enough it can also be used as model for understanding social behavior of humans.
Žaidimo esmė yra elementari, bet kaip nebūtų keista – teisingo sprendimo ar laiminčios strategijos čia nėra ir negali būti. Įdomu ir tai, kad toks elementarus modelis gali būti panaudotas žmonių visuomeniškumo ir egoistiškumo supratimui 1.
Research Council of Lithuania has announced a call for applications for students’ research practice in Lithuania in summer of 2013. The contributors towards Physics of Risk website, dr. (HP) Vygintas Gontis and PhD student Aleksejus Kononovičius, offer two topics for the research practice. The offered topics are mainly based on the following topics, previously published on this website:
Previously we wrote about randomly generated attractors. That time we have used Wolfram CDF technology to power the interactive applet. This technology has a serious drawback that you have to have installed specific additional software to be able to use it. As of now we have replaced the old app with HTML5-based interactive applet. This applet can be run on almost any modern web browser without a need to have any additional software preinstalled.
The new applet can be found in the old post and here.
In the 1738, Daniel Bernoulli, the very same known for his contribution to fluid dynamics, in his paper in the “Commentaries of the Imperial Academy of Science of Saint Petersburg” described an interesting paradox. Let us assume that we have a fair 50-50 game in which the host tosses a coin until the tail appears. After each toss he pays a player (where is a number of the toss) of money. The problem in question is – what is an optimal price for the game? Namely how much money the host should ask from a player, that he would be still motivated to play the game, yet also preventing unnecessary losses by the host. Continue reading “The Saint Petersburg paradox” »
The quantitative comparison of economic growth of various states is still an ambiguous task. Economists and statisticians use various estimates of Gross Domestic Product (GDP) taking into account inflation, population, exchange rates etc. Here we present a graphical comparison of GDP growth of various states aimed at the estimation of relative input of various states into regions or the world economy and at the measure of economic convergence. We choose the estimate of GDP in common currency US dollars calculated in current prices and current exchange rates. In order to compare different size states we use GDP normalized per capita. Such data is available at the World Bank Database. Continue reading “V. Gontis, A. Kononovicius: The phenomenon of economic growth of Baltic states” »
Here, on the Physics of Risk, we frequently talk about two essential statistical features of the time series – probability and spectral densities. The probability density function should well known to our readers – it is related to the distribution of time series values. On the Physics of Risk we have also a Lithuanian-only article on this topic (see it here). So the time has come to discuss the power spectral density. Continue reading “Power spectral density (part 1)” »
Previously on Physics of Risk we have wrote about Lotka-Volterra equations. At that time we didn’t provide an interactive applet with the text. Only recently we have updated the text and provided an interactive Wolfram CDF applet. This applet was replaced by HTML5 app, yet it is still available for download.
In classical physics differential equations is the main tool to mathematically describe dynamical systems. Having obtained the mathematical descriptions of the system we should be able to predict the evolution of the system. It is noted that the evolution of the classical systems is pretty trivial – no matter what the initial condition is the system will “find” the stable state. Usually dissipative forces (such as frictions) are to be blamed for this. Though not all systems are so simple… Continue reading “Randomly generated strange attractors” »