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We study two aspects of the detrended .uctuation analysis (DFA) method, namely the scaling behavior of the leading terms of the best-0t polynomials and the detection of trends. We show analytically and numerically that the standard deviation of the leading terms of the best-0t polynomials used in DFA displays scaling behavior. Furthermore, we demonstrate that the distribution of these terms can be used to reveal the presence of trends in the data. We also argue that this distribution can be used as a sensitive tool for identifying weak trends. c 2001 Elsevier Science B.V. All rights reserved.

A prey–predator system with intelligent pursuit and evasion is studied by means of computer simulations. It is found that the model exhibits a coexistence state between prey and predators. In this state and depending on the parameters, the system may evolve toward two different regimes, characterized by the behavior of the prey–predator population. Whitin the oscillatory (fixed point) regime the specie's density changes periodically (remains constant), respectively. The transition between such regimes is rationalized in terms of a dynamic percolation process.

The classic Katz–Lebowitz–Spohn (KLS) model is a lattice gas driven by an external field. In this paper, we study the critical behavior of the KLS model driven by an oscillatory field of strength E and period τ by means of both, Monte Carlo simulations and a coupled-map-lattice mean-field approach. It is found that, keeping the amplitude constant and changing the period, a novel phase transition between a non-equilibrium-stationary-state and an almost equilibrium-stationary-state takes place at a certain critical value τc.

A stochastic game of life (SGL) which simulates the dynamic evolution of a society of living organisms in the presence of noise is introduced. The SGL exhibits a very rich critical behavior with many critical edges at the irreversible phase transitions: extinction—life and life—overcrowding. Furthermore, within the living phase, critical edges at transitions between chaotic and frozen life are also found.

Transport properties are investigated by means of Monte Carlo simulations on percolating clusters obtained depositing very hot dimers in two dimensions. The properties are discussed within the framework of the random walks arguments. The diffusion exponent dw and the spectral dimension ds exhibit finite size effects and their asymptotic values in the thermodynamic limit differ from both the corresponding to standard percolation and Euclidean lattices.

The critical behavior of percolating clusters formed upon random sequential adsorption of hot dimers in two dimensions is investigated by means of Monte Carlo simulations and discussed on the basis of finite-size scaling theory. The critical thresholds depend on the flying distance (R) of the monomers formed upon hot dimer adsorption. The model belongs to the same universality class as standard percolation as judged by the evaluated critical exponents. The hot dimer adsorption mechanism introduces an additional characteristic distance (rc = 2R + 1) to the model, which is reflected in the microscopic structure of the percolating clusters for r < rc. The macroscopic structure, for r ⪢ rc, corresponds to standard percolation.