The flux of the chaotic transport of asteroidal and meteoritic material from the main belt to the Earth vicinities depends on the extents of chaotic domains (corresponding to relevant mean motion and secular resonances) in space of orbital elements of the transported matter. These extents vary, most prominently on the 50-100 ka time scale, due to variations of orbital elements of major planets. The extents' variations are being studied, both numerically and analytically, within the problem in the orbital dynamics of asteroids near the 3/1 mean motion resonance with Jupiter. The numerical study is performed by means of computations of the maximum Lyapunov characteristic exponents of the trajectories on a fine grid of starting values on a suitably defined representative section of phase space. The analytical consideration is based on the separatrix map theory in frames of a model of the resonance as a perturbed nonlinear pendulum. The flux of NEAs can be modulated as well by the variability of the chaotic zones associated with Martian mean motion resonances and the secular resonance V₆. A problem is considered whether the modulation of the chaotic transport of NEAs could be responsible for the still puzzling dominant near-periodicity of 100 ka observed in the Quaternary paleoclimatic records.