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Simulations are performed according to the Axelrod model of culture dissemination, with modified mechanism of repulsion. Previously, repulsion was considered by Radillo-Diaz et al (Phys. Rev. E 80 (2009) 066107) as dependent on a predefined threshold. Here the probabilities of attraction and repulsion are calculated from the number of cells in the same states. We also investigate the influence of some homogeneity, introduced to the initial state. As the result of the probabilistic definition of repulsion, the ordered state vanishes. A small cluster of a few percent of population is retained only if in the initial state a set of agents is prepared in the same state. We conclude that the modelled imitation is successful only with respect to agents, and not only their features.

Our recent minimal model of cooperation (P. Gawronski et al, Physica A 388 (2009) 3581) is modified as to allow for time-dependent altruism. This evolution is based on reputation of other agents, which in turn depends on history. We show that this modification leads to two absorbing states of the whole system, where the cooperation flourishes in one state and is absent in another one. The effect is compared with the results obtained with the model of indirect reciprocity, where the altruism of agents is constant., Comment: 10 pages, 4 figures

In our recent model, the cooperation emerges as a positive feedback between a not-too-bad reputation and an altruistic attitude. Here we introduce a bias of altruism as to favorize members of the same group. The matrix F(i,j) of frequency of cooperation between agents i and j reveals the structure of communities. The Newman algorithm reproduces the initial bias. The method based on differential equations detects two groups of agents cooperating within their groups, leaving the uncooperative ones aside., 8 pages, 2 figures

The norm game (NG) introduced by Robert Axelrod is a convenient frame to disccuss the time evolution of the level of preserving norms in social systems. Recently NG was formulated in terms of a social contagion on a model social network with two stable states: defectors or punishers. Here we calculate the critical line between these states on the plane of parameters, which measure the severities of punishing and of being punished. We show also that the position of this line is more susceptible to the amount of agents who always punish and never defect, than to those who always defect and never punish. The process is discussed in the context of the statistical data on crimes in some European countries close to Wroc{\l}aw - the place of this Conference - around 1990., Comment: 9 pages, 5 figures

Simulations are reported on the Ising two-dimensional ferromagnet in the presence of a special kind of noise. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly selected n spins at each timestep. This is introduced to mimic the self-organized criticality as a model influence of a complex environment. We reproduced the phase transition similar to the case of P(n) = constant. Above some value of the noise amplitude the magnetisation tends to zero; otherwise it remains constant after some relaxation. Information of the initial spin orientation remains preserved to some extent by short-range spin-spin correlations. The distribution of the times between flips is exponential. The results are discussed as a step towards modeling of social systems., Comment: 8 pages including 8 figures

The Heider theory of cognitive dissonance in social groups, formulated recently in terms of differential equations, is generalized here for the case of asymmetric interpersonal ties. The space of initial states is penetrated by starting the time evolution several times with random initial conditions. Numerical results show the fat-tailed distribution of the time when the dissonance is removed. For small groups (N=3) we found some characteristic patterns of the long-living states. There, mutual relations of one of the pairs differ in sign., Comment: 8 pages, 4 figures

Long-range magnetostatic interaction between wires strongly depends on their spatial position. This interaction, combined with applied tensile stress, influences the hysteresis loop of the system of wires through the stress dependence of their coercive fields. As a result, we obtain a set of stable magnetic states of the system, dependent on the applied field, applied stress and mutual positions of the wires. These states can be used to encode the system history., Comment: 16 pages, 8 figures. Presented at III Joint European Magnetic Symposia, San Sebastian, 26-30 June, 2006

Formation of random network of DNA strands is simulated on a two-dimensional triangular lattice. We investigate the size distribution of pores in the network. The results are interpreted within theory of percolation on Bethe lattice., Comment: 8 pages, 6 figures. Corrected the reference value of the exponent tau

Numerical simulations are performed for the stick-slip motion in the Burridge-Knopoff model of one block. Calculated amplitude increases with the driving velocity. We argue that this effect can be a criterion to distinguish between the stick-slip and pure slip oscillations., 8 pages, 3 figures

We present the simulation of the time evolution of the distance matrix. The result is the node-node distance distribution for various kinds of networks. For the exponential trees, analytical formulas are derived for the moments of the distance distribution., presented during the 37-th Polish Physicists' Meeting, Gdansk, Poland, 15-19 Sep. 2003, 6 pages, 3 figures

Dynamics of nanoscopic arrays of monodomain magnetic elements is simulated by means of the Pardavi-Horvath algorithm. Experimental hysteresis loop is reproduced for the arrays of Ni, with the period 100 nm and the mean coercive field 710 Oe.We investigate the box-counting fractal dimension of a cluster of elements with given orientation of magnetic moments. No fractal behavior is found. Also, the damage spreading technique is applied to check the criticality. We find that the consequences of a local flip of one magnetic element remainlimited to a finite area. We conclude that the system does not show a critical behavior., 8 pages, 5 figures

A three-blocks Burridge-Knopoff model is investigated. The dimensionless velocity-dependent friction force $F(v)\propto (1+av)^{-1}$ is linearized around $a=0$. In this way, the model is transformed into a six-dimensional mapping $\mathbf{x}(t_{n})\to \mathbf{x}(t_{n+1})$, where $t_n$ are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For $a0.1$, the motion becomes chaotic. These results are true for the linearized mapping, linearized numerical and non-linearized numerical solutions., 11 pages, 12 figures, 30th Leeds-Lyon Symposium on Tribology, Sep. 2-5, 2003

We show that the structure of a growing tree preserves an information on the shape of an initial graph. For the exponential trees, evidence of this kind of memory is provided by means of the iterative equations, derived for the moments of the node-node distance distribution. Numerical calculations confirm the result and allow to extend the conclusion to the Barabasi--Albert scale-free trees. The memory effect almost disappears, if subsequent nodes are connected to the network with more than one link., Comment: 9 pages, 9 figures

A social system is represented by the Barabasi-Albert model. At each node of the graph, an Ising spin is placed with antiferromagnetic interaction between connected nodes. ... The system changes only at its initial stages. ... The conclusions are illustrated with events from recent European history where after some strong change a rather immobile society evolved., 7 pages sociophysics including 6 figures

In the thermodynamic limit, a probabilistic cellular automaton can be approximated by a deterministic nonlinear map. Here we construct such a map for the forest fire problem. The construction is based on the results of the Monte Carlo simulation, performed on a square lattice of million cells. The results of the calculation are analyzed by means of the Hoshen--Kopelman algorithm (HKA). The only parameter of the map describes the probability that a tree appears at an empty cell during one time step. The obtained map seems to be non-differentiable at the percolation threshold. The Lyapunov exponent for the map is positive. Also, we found the cycle of length three by means of the method of symbolic dynamics. The results are illustrated by the experimental data on the forest fires in Canada in years 1970--2000. Although these data are fortunately far from thermodynamic limit, their qualitative character is reproduced for smaller lattices., 9 pages, 10 figures

A network of agents cooperate on a given area. Time evolution of their power is described within a set of nonlinear equations. The limitation of resources is introduced via the Verhulst term, equivalent to a global coupling. Each agent is fed by some other agents from his neighborhood. Two subsequent stages of the time evolution can be observed. Initially, the richness of everybody increases distinctly, but its distribution becomes wide. After some transient time, however, resources are exhausted. Richness of some agents falls to zero and they are eliminated. Cooperation becomes less effective, what leads to subsequent falls. Finally, small percent of agents survive in a steady state. We investigate, how the cooperation influences the rate of surviving., 6 pages, 2 figures

The Heider balance is a state of a group of people with established mutual relations between them. These relations, friendly or hostile, can be measured in the Bogardus scale of the social distance. In previous works on the Heider balance, these relations have been described with integers 0 and $\pm1$. Recently we have proposed real numbers instead. Also, differential equations have been used to simulate the time evolution of the relations, which were allowed to vary within a given range. In this work, we investigate an influence of this allowed range on the system dynamics. As a result, we have found that a narrowing of the range of relations leads to a large delay in achieving the Heider balance. Another point is that a slight shift of the initial distribution of the social distance towards friendship can lead to a total elimination of hostility., 13 pages, 3 figures