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We present a 2-dimensional time-dependent simulation based on Parker’s transport equation (PTE) describing the propagation of energetic astroparticles – cosmic rays (CR) in the heliosphere. PTE is a second order partial differential equation containing four major processes: diffusion, convection, drift, and adiabatic cooling responsible for modulation of the CR flux in the heliosphere. We implement in the numerical simulation, a few physical parameters as the tilt angle,    $\delta $   δ    , of the heliospheric current sheet (HCS), module,    $B$   B    , of the interplanetary magnetic field (IMF), and variations of drift effect of the CR particles with solar activity (SA). Our approach is the implementation of two independent parameters (proxies),    $\gamma $   γand    $\nu $   ν    . The parameters    $\gamma $   γand    $\nu $   νare calculated from various independent sources,    $\gamma $   γ    , from neutron monitors (NM) daily data, and    $\nu $   ν    , using the IMF hourly data. The solutions of PTE obtained from our numerical model are compared with the variations of the CR flux recorded by NMs. We prove the existence of a varying delay time (DT) between the changes of galactic cosmic ray (GCR) intensity and the parameters characterizing SA. Based on our investigation, we obtained different DTs in Solar Cycles 21 and 23. We conclude that the calculated DTs, after comparison with the observed DTs, are useful parameters for the study of GCR transport in the heliosphere.

Modeling the Time Delay Problem of Galactic Cosmic Ray Flux in Solar Cycles 21 and 23