Dinámica de Sistemas: Estructuras genéricas (Crecimiento en forma de S) HD
Growth Dynamics and Simulation of Populations
Introduction to Growth Structures
- The tutorial begins with an overview of growth structures, specifically the "S-shaped" or sigmoid growth curve, which illustrates how populations grow over time.
- Initially, growth is exponential until it reaches an inflection point where the curve approaches equilibrium.
Examples of Sigmoid Growth
- Systems exhibiting this behavior include rumor propagation, new product sales, epidemics, and populations in limited resources.
- A simulation will be created to demonstrate population growth under limiting factors using a model for rabbit populations in confined areas.
Model Creation for Population Simulation
- The simulation parameters are set: initial time at zero years and final time at one hundred years with a time step of 0.625 years.
- Key variables include:
- Initial rabbit population set to 1
- Birth rate defined as normal births per year (1.5)
- Mortality rates based on life expectancy.
Population Dynamics Equations
- The model incorporates equations for birth and death rates:
- Birth rate calculated as a function of current population density.
- Death rate determined by the ratio of current population to life expectancy.
Feedback Loops in Population Growth
- Initially, positive feedback from births dominates leading to exponential growth; however, as resources become scarce, negative feedback from deaths becomes more significant.