Frequencies and resonances around L4L_4 in the elliptic restricted three-body problem

The stability of the Lagrangian point $L_4$ is investigated in the elliptic restricted three-body problem by using Floquet's theory. Stable and unstable domains are determined in the parameter plane of the mass parameter and the eccentricity by computing the characteristic exponents. Frequencies of motion around $L_4$ have been determined both in the stable and unstable domains and fitting functions for the frequencies are derived depending on the mass parameter and the eccentricity. Resonances between the frequencies are studied in the whole parameter plane. It is shown that the 1:1 resonances are not restricted only to single curves but extend to the whole unstable domain. In the unstable domains longer escape times of the test particle from the neighbourhood of $L_4$ are related to certain resonances, but changing the parameters the same resonances may lead to faster escape

Signal generation and propagation in the olfactory bulb: Multicompartmental modeling

AbstractThe generation and propagation of action potentials in the two major cell types of the olfactory bulb, i.e., in the mitral and granule cells, are simulated by applying the multicompartmental modeling technique. The specific effects of the individual ionic currents, the propagation of the signals through the compartments, and several dynamic phenomena occurring in small networks (such as synchronized oscillation due to excitatory and inhibitory coupling) have been demonstrated

Forward and Backward Modelling: From Single Cells to Neural Population and Back

Some aspects of forward and backward neural modelling are discussed, showing, that the neural mass models may provide a “golden midway” between the detailed conductance based neuron models and the oversimplified models, dealing with the input–output transformations only. Our analysis combines historical perspectives and recent developments concerning neural mass models as a third option for modelling large neural populations and inclusion of detailed anatomical data into them. The current source density analysis and the geometrical assumption behind the different methods, as an inverse modelling tool for determination of the sources of the local field potential is discussed, with special attention to the recent results about source localization on single neurons. These new applications may pave the way to the emergence of a new field of micro-electric imaging

The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.Comment: 16 pages, 8 figures, appeared in the open-access journal Symmetry (special issue: Astronomy and Symmetry

A fast method to identify mean motion resonances

The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance variable, an efficient method is introduced and described here, by which mean motion resonances can be easily find without any a priori knowledge on them. The efficiency of this method is clearly demonstrated by using known exoplanets engaged in mean motion resonances, and also some members of different families of asteroids and Kuiper-belt objects being in mean motion resonances with Jupiter and Neptune respectively.Comment: 7 pages, 13 figures, accepted by Monthly Notices of the Royal Astronomical Societ