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Jaroslaw Bialecki
How do we respire?
Is the transport of oxygen in the lung bubbles caused only by diffusion or also by micro-vortices?
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Janusz Holyst
Limits of time-delayed feedback control
General features of stability domains for time-delayed feedback control exist, which can be predicted analytically. We clarify, why the control scheme with a single delay term can only stabilize orbits with short periods or small Lyapunov exponents, and derive a quantitative estimate. The limitation can be relaxed by employing multiple delay terms. In particular, the extended time delay autosynchronisation method is investigated in detail. Analytic calculations are in good agreement with results of numerical simulations and with experimental data from a nonlinear diode resonator.
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Krzysztof Kacperski
Formation of opinions under the influence of competing agents - a mean field approach
We study a model of opinion formation based on the theory of social impact and the concept of cellular automata. The case is considered when two strong agents influence the group: a strong leader and an external social impact acting uniformly on every individual. There are two basic stationary states of the system: cluster of the leader's adherents and unification of opinions. In the deterministic limit the variation of parameters like the leader's strength or external impact can change the size of the cluster or, when they reach some critical values, make the system jump to another phase. In the presence of noise (social temperature) the rapid changes can be regarded as the first order phase transitions. When both agents are in a kind of balance, a second order transition and critical behaviour can be observed. Analytical results obtained within a mean field approximation are well reproduced in computer simulations.
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Krzysztof Kacperski
Opinion formation model with strong leader and external impact: a mean field approach
We study a model of opinion formation based on the theory of social impact and the concept of cellular automata. The case is considered when two strong agents influence the group: a strong leader and an external social impact acting uniformly on every individual. There are two basic stationary states of the system: cluster of the leader's adherents and unification of opinions. In the deterministic limit the variation of parameters like the leader's strength or external impact can change the size of the cluster or, when they reach some critical values, make the system jump to another phase. For a certain range of parameters multistability and hysteresis phenomena are observed. In the presence of noise (social temperature) the rapid changes can be regarded as the first order phase transitions. When both agents are in a kind of balance, a second order transition and critical behaviour can be observed. Another kind of noise induced transitions are the inverses (flips) of the unified group opinion due to random flips of the leader's opinion. Analytical results obtained within a mean field approximation are well reproduced in computer simulations.
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Marek Szydowski, Adam Krawiec
Scientific cycle model with delay
In this paper we propose to analyze the growth of scientific results in terms of infinite dynamical system theory. We use functional differential equations to model evolution of science in the sociological aspect. In our model time-to-build of scientific notions (understanding) is included. It is a similar concept to the Levy-Blond recasting process. We show that the delay parameter describing time needed to learn and apply the past scientific results to new discoveries plays a crucial role in generating the cyclic behaviour via the Hopf bifurcation scenario. Our model extends the de Sola Price model by including dying of results as well as by incorporating time-to-build notion.
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Dimitris Kugiumtzis
Lack of Robustness of the surogate data test:
Examles from Physiology and Finance
The direct application of nonlinear tools (such as the estimation of correlation dimension or the Lyapunov exponents) to real time series, seems to give rarely convincing evidence on the existence of nonlinear dynamics.
On the other hand, the indirect approach, attempting to exclude that the data are ''linear'', has gained much interest in the last years. This is typically done by using the method of surrogate data. The most general null hypothesis in this respect is that the data are generated by a Gaussian (linear) process undergoing a possibly nonlinear static transform.
The null hypothesis is tested by comparing the value of an estimate of a nonlinear characteristic derived from the original data with the corresponding values computed from a set of surrogate time series representing the null hypothesis.
The generated surrogate data do not always represent completely this null hypothesis. Often the original linear correlations may not be preserved in the surrogate data, which can effect on the result of the test. The rejection of the null hypothesis may also depend on the applied nonlinear method and the choice of the method parameters. Here, we argue against reported success of the test on physiological and financial data and claims of evidence of nonlinearity based on a single nonlinear statistic.
In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on arbitrarily selected EEG data and stock index data suggest that rejections of the null hypothesis vary with the method and its parameters and depend also on the algorithm generating the surrogate data.
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Gábor Kutrovátz
From the Extropy of the Universe to the Economic Constraints
Here I try to build a connection between cosmology and economy from a thermodynamic point of view.For this purpose, I introduce the notion of extropy, which is the distance of a physical system from its equilibrium state on the entropic scale.
The extropy of the Universe (the distance from the state of Heat Death) is determined by the interaction of its material components (expanding in their volume), and this extropy determines the rate of thermodynamic processes.
I hope to be able to outline some similarities between cosmological and economic systems, giving a parallel interpretation of a physical and an economic problem.

1. First, I would like to show that the application of equilibrium thermodynamics to cosmology is fruitful. I offer some results that I (following G. Marx, R. Alpher and K. Martinás) have worked out in this field. 
2. Second, I would like to hint some ideas that should illustrate why the analogy between thermodynamics and economics cannot be forced too far, BUT the analogy between cosmology and economics looks more promising.
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Lorenzo Escot Mangas, Ricardo Gimeno Nogués, Ruth Mateos de Cabo, Elena Olmedo Fernández, Jose Ramón Sánchez-Galán
Nonlinearities in economic convergence. The German-Spanish case in fixed rates and stockexchange markets.

One of the main targets for the European Union is to level the different economic conditions and opportunities all over the countries of the Union -that is what we call real convergence. It is essential to know if real convergence of economies is being reached, and if nonlinearities are present in this union process in orden to try to explain better the behaviour of that process and the presence of similar patterns among the different countries.
On the other hand, a way to look for real convergence lies on studying the evolution of the stock market indexes and the interest rates series of the long-term bond that the different countries of the European Union may have. Germany has been chosen, for obvious reasons, as a reference country for the Spanish convergence.
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Dietmar Meyer
Human Capital in a Non-Linear Model of Economic Growth
As a result of recent research in the field of growth theory the attention was directed again to the rule of human capital in the process of economic development. In part one an overview will be given about the so-called "new" growth theory. In part two the three-sector-modell will be introduced and interpreted. The main point is the analysis of the stability properties of this modell, expressing the behavior of human capital, the development of real capital and consumption in the neighborhood of the equilibrium. The last part contains conclusions for the economic policy in countries with different levels of economic development, especially for the transformation countries in East-Middle-Europe.
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Stanislaw Sieniutycz
Minimum of Entropy Generation as a General Evolution Criterion for Nonlinear Structured Systems with Fixed Boundaries
The purpose of our presentation is a general thermodynamic framework for balance and kinetic equations of structured heterogeneous systems and chemical networks which is consistent with the second law of thermodynamics. Methods effective in classical irreversible thermodynamics of single-phase systems are here extended to include boundary discontinuities, surface reactions and interface transports in multiphase systems. Complex multiphase and multireaction systems are analyzed by methods of the network (system) theory in which topological and graphical methods of electrical networks are extended to quite general energo-chemical systems. Chemical Ohms law links chemical force (affinity) and chemical flux (reaction rate), and chemical conversions follow simple rules of the algebra for chemical resistances. There are two main methods coming from thermodynamics of single-phase systems, which can effectively be applied to complex structured systems. The first method starts with the derivation of balance equations for mass, energy and momentum and terminates at the entropy balance; from the knowledge of the entropy source ss kinetic laws are postulated. Yet, our main objective is the second (newer) method which is based on the variational formulation of second law and concept of nonlinear chemical resistance. It is an optimization method in which an entropy functional is minimized to predict kinetic laws and secure appropriate balance equations. The method does not postulate linearity; rather it rests on state-dependent dissipation functions. It follows that the variational method assures classical nonlinear kinetics of mass action and nonlinear set of diffusion-reaction equations under the condition of local thermal equilibrium. Still local disequibria can be predicted which are shown to be responsible for onset of interfacial and bulk instabilities. Hamiltonian form of transport equations and laws of chemical kinetics is valid, which is efficient to accommodate nonlinear effects.
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Wolfgang Weidlich
Recurrence in Physical and Social Systems.
The problem of the relation between recurrence and irreversibility is an old and universal one: It has been discussed by philosophers, physicists, historians, and social scientists.
After briefly mentioning philosophical formulations of the problem, the controversy, being deeply inherent in the notions of Statistical Physics, is discussed in terms of Poincare's recurrence theorem versus irreversible equations such as the Boltzmann equation. The conclusion is that the neglection of certain correlations, i.e. an approximation, leads from recurrence to irreversibility.
Thereupon the inverse problem is considered, in which manner recurrent, in particular periodic or quasi-periodic sub-processes can appear to be embedded in a globally irreversible process. Some approaches how to trace and recognize embedded recurrent (and even periodic) sub-processes are discussed.
Finally selected examples of model-based (quasi-) periodic processes in social systems are presented. They belong to the sectors demography (migration), sociology (group dynamics), and economics (demand dynamics).
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