The rabbit model is a classic simulation tool that is widely used in fields such as ecology, mathematics and computer science. The model was originally proposed by renowned mathematician Francis Gauss to simulate the population growth and reproductive behavior of rabbits. Through simple assumptions, the rabbit model shows the dynamic characteristics of biological populations over time, revealing the balance and change in the ecosystem.

In the rabbit model, population growth usually follows the principle of exponential growth. Assuming the environment is well-resourced and rabbits have no natural predators, the population will increase exponentially under ideal conditions. Each pair of rabbits is able to produce multiple offspring each year, which in turn reproduce at the right age to form an ever-expanding population. This scenario is valid in theory, but it is often limited by the limited resources and the carrying capacity of the environment in the actual ecosystem.

As populations continue to grow, environmental resources will gradually be depleted, competition will intensify, and population size will begin to be limited. At this point, the rabbit model introduces a concept called "environmental carrying capacity." When the population reaches the carrying limit of the environment, the birth rate will decrease and the death rate will rise, resulting in the population stabilizing. This phenomenon can be described by the S-shaped curve, the initial rapid growth will eventually slow down and maintain a relatively stable level.

The rabbit model can also introduce other factors, such as the presence of predators, the spread of disease, and the influence of the food chain, to make the model more complex and realistic. These factors can lead to periodic fluctuations in the population and even the risk of extinction. By performing numerical simulations and parameter adjustments on rabbit models.