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We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.

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The trajectories of propagating self-organized, well-localized solitary patterns (dissipative solitons) in the form of electrical current filaments are experimentally investigated in a planar quasi-two-dimensional dc gas-discharge system with high Ohmic semiconductor barrier. Earlier phenomenological models qualitatively describing the experimental observations in terms of a particle model predict a transition from stationary filaments to filaments traveling with constant finite speed due to an appropriate change of the system parameters. This prediction motivates a search for a drift bifurcation in the experimental system, but a direct comparison of experimentally recorded trajectories with theoretical predictions is impossible due to the strong influence of noise. To solve this problem, the filament dynamics is modeled using an appropriate Langevin equation, allowing for the application of a stochastic data analysis technique to separate deterministic and stochastic parts of the dynamics. Simulations carried out with the particle model demonstrate the efficiency of the method. Applying the technique to the experimentally recorded trajectories yields good agreement with the predictions of the model equations. Finally, the predicted drift bifurcation is found using the semiconductor resistivity as control parameter. In the resulting bifurcation diagram, the square of the equilibrium velocity scales linearly with the control parameter.

Here, we report on the experimental observation of a rotating hexagonal pattern in a continuous dissipative medium. The system under investigation is a planar dielectric barrier gas-discharge cell. The pattern consists of a set of current filaments occupying the whole discharge area and rotating as a rigid body. The symmetry of the rotating hexagons is lower than the symmetry of the stationary hexagonal pattern. We study the dynamics of the pattern, especially peculiarities of its rotational velocity. The temperature of the gas is found to be an important quantity influencing the rotating hexagons.