The beam-beam effect, or beam-beam interaction, is recent research conducted in many areas around the world, from European laboratories to American institutes. Basically the problem concerns the passage of proton beams which causes many different types of effects, sometimes even unexpected ones. Aside from particles rubbing against each other, the collision speed of protons usually generates a certain amount of energy. Today the issue is to focus on modifying new colliders to improve the effectiveness of the machines. The study of the beam-to-beam effect involves particle colliders that determine the collision speed of protons. One of the commonly used colliders is the LHC, which stands for Large Hadron Collider. The LHC is an accelerator that brings protons and ions colliding at higher energies than ever before. This will allow scientists to penetrate even deeper into the structure of matter and recreate the conditions prevailing in the early universe, immediately after the "big bang". It is represented by a thick Gaussian lens and the ring is described by a 9th order Taylor map. At the single particle level we compare the dynamic aperture with and without the beam-to-beam effect. At the multiparticle level, using a “strong-strong” description of the beam-beam interaction, we compare the collision rate with a linear lattice map and with the full nonlinear map. The LHC is used at CERN, the world's largest physical center for particle physics that explores what matter is made of and what forces hold it together. Many different models have been conducted previously for this effect, but most of them often ignore the longitudinal motions of the particles, meaning they only look for stationary solutions, or assume that a beam contains a larger number of particles. These are generally known as "weak-strong" simulations. The LHC under development is a "strong-strong" simulation in that it treats both beams equally and allows them to have arbitrary relative intensities. It is dynamic in that it models the movement turn after turn by looking for coherent oscillations in the shape of the beam. It uses a variety of methods to calculate electric fields so that it can function as quickly as possible in every situation it encounters. Inside the LHC, there is usually a storage ring that acts as an accelerator that repeatedly collides clusters of particles by storing the clusters in the collider for a certain period of time. When firing particles, the collider aims for a very high collision rate or brightness.