As the observations of highly flattened galaxies, including the Milky Way, and gravitational N-body simulations show, the central parts of these systems at distances of, say, r < 0.5-0.7 kpc from the center rotate slowly, and their local circular velocities of regular rotation become less than (or comparable to) the residual (random) velocities. In such a thin, practically nonrotating, pressure-supported central disk, a typical star moves along the bending, perpendicular to the equatorial plane layer, under the action of two forces acting in opposite directions: the destabilizing centrifugal force, c, and the restoring gravitational attraction, g. Obviously, fierce instabilities of the buckling kind developing perpendicular to the plane may not be avoided if Fc > Fg. The latter condition is none other than the condition of the so-called firehose electromagnetic instability in collisionless plasmas. The source of free energy in the instability is the intrinsic anisotropy of a velocity dispersion ("temperature"). It seems reasonable that this is a natural mechanism for building a snake-shaped radio structure, which has recently been observed by Zhao and coworkers in the central region of the spiral starburst galaxy NGC 2146 with the Very Large Array at an angular resolution of 2''. In the current paper, in order to investigate the dynamics of the central region, N-body simulations of the firehose-type bending instability are presented for this galaxy. Use of concurrent computers has enabled us to make long simulation runs using a sufficiently large number of particles in the direct summation code, N ~ 20,000. In contrast to all previous N-body simulations of bending instabilities, we show how bending structures may be longer lived in real starburst galaxies than in the computer models. The simulations clearly confirm the qualitative picture and, moreover, are in fair quantitative agreement with the theory. A theoretical prediction is confirmed that the instability is driven by an excess of plane kinetic energy of random motions of stars, when the ratio of the dispersion of radial velocities of stars in the plane cr to the velocity dispersion in the perpendicular direction cz is large enough, cr ≳ 0.6cz, in other words, if the thickness of the stellar disk h ∝ cz is small enough. The extent to which our results on the stability of the disk can have a bearing on observable spiral galaxies with a high star formation rate in the central parts is discussed.