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EN
A cellular automaton model is presented in order to describe mutual interactions among the individuals of a population due to social decisions.The scheme is used for getting qualitative results, comparable to field experiments carried out on a population of ants which present an aggregative behavior. We also present a second description of a biological spatially structured population of N individuals by a system of stochastic differential equations of Ito type. A 'law of large numbers' to a continuum dynamics described by an integro-differential equation is given.
EN
The self-gravitating electrodynamic stability of an annular fluid jet (a fluid jet having a tar cylinder as a mantle) pervaded and surrounded by periodic time dependent electric field has been developed. The perturbed system equations describing the model motion is turned to a second integro-differential Mathieu equation. The self-gravitational force is destabilizing only for small axisymmetric perturbation modes. The radii tar-fluid cylinders ratio plays an important role in stabilizing the model. The periodic longitudinal electric field is strongly destabilizing for all perturbation modes. However under some restrictions (independent of the electric field amplitude), it is found that the electric field frequency has a stabilizing influence and that influence suppresses almost the instability character of the annular jet. In contrast to the same model pervaded by classical (constant) electric field, the self-gravitational instability will never be suppressed whatever is the strength of the pervaded electric field. The present analyses have been performed on the basis of the Lagrangian energy principle which it was not an easy job.
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