The rabbit model is a classical mathematical and biological model commonly used to describe the growth and reproduction of a population. Based on simple assumptions, this model reveals the nature of changes in population dynamics by abstracting rabbit reproductive behavior.
In the rabbit model, the most basic assumption is that rabbits breed in an ideal environment, and their reproduction rate is positively correlated with the current population size. Suppose each pair of rabbits is able to produce a pair of bunnies each month, and these bunnies also start breeding after two months. This model can be expressed as a recursive relationship, forming a simple sequence that shows the exponential increase in rabbit numbers over time.
However, real-world ecosystems are not always ideal. The rabbit model does not consider resource constraints and environmental carrying capacity in classical dynamics. As rabbit numbers increase, resources such as food, water and habitat will become strained, causing population growth to slow down or even decline. This phenomenon can be corrected by introducing the concept of environmental bearing capacity. By increasing the resource constraint factor, the model becomes more realistic, and the population tends to a stable value, called an equilibrium state.
During the simulation, the rabbit model can also introduce other variables, such as the influence of predators and the spread of disease. Once these complexities are introduced, the model's performance becomes more complex and represents larger changes in the real ecosystem. At this time, the straight line of geometric growth of the population will become tortuous, and there may be periodic fluctuations or unstable oscillations. Such a model is not only of great significance to ecological research, but also plays a reference role in dynamic analysis involving economics, sociology and other fields.