# • Find one example of first-order reinforcing/balancing feed…

• Find one example of first-order reinforcing/balancing feedback system. You cannot use an example from class or the textbook. • Using Vensim, build the model. – Don’t forget to set the time frame, units, and initial value of the stock. • Submit your Model to BBLearn (.mdl file)

**Answer**

In the field of system dynamics, feedback systems play a crucial role in elucidating the natural behavior of various complex phenomena. These systems can be broadly classified into two types: reinforcing feedback systems and balancing feedback systems. Reinforcing feedback systems amplify or reinforce the effects of an initial change, leading to continued growth or decay. On the other hand, balancing feedback systems aim to maintain stability by counteracting or balancing out changes.

To fulfill the requirement of finding an example of a first-order reinforcing/balancing feedback system, I will focus on the domain of population dynamics. Specifically, I will consider the interaction between predator and prey populations, which is often depicted by the Lotka-Volterra equations.

The Lotka-Volterra equations are a mathematical model that characterizes the dynamics of predator-prey relationships. These equations, proposed by Alfred J. Lotka and Vito Volterra independently, illustrate how the populations of predators and prey reciprocally influence each other.

Let’s consider a hypothetical scenario involving wolves as predators and rabbits as prey. The population of rabbits (R) serves as the prey, while the population of wolves (W) represents the predators. In this system, the growth of the rabbit population is reinforced by the absence of predators, while the growth of the wolf population is reinforced by the availability of prey.

The Lotka-Volterra equations for this system can be represented as follows:

dR/dt = αR – βRW

dW/dt = δRW – γW

In these equations, the rate of change of the rabbit population (dR/dt) depends on the growth rate of rabbits (αR), which represents their natural reproduction, and the predation rate (βRW), where β represents the efficiency of predation. The rate of change of the wolf population (dW/dt) depends on the predation rate (δRW), where δ represents the efficiency of prey capturing, and the natural mortality rate of wolves (γW).

This system exhibits a balancing feedback loop. When the rabbit population increases, the availability of prey becomes abundant, resulting in an increase in the wolf population. However, as the wolf population grows, the predation rate also increases, leading to a decrease in the rabbit population. This decrease in the rabbit population then causes a decline in the wolf population due to scarce food resources. This cyclic nature of predator-prey interactions indicates a balancing feedback system.

To gain deeper insights into the behavior of this predator-prey system, we can utilize system dynamics software such as Vensim to create a model. By specifying the values for parameters like α, β, δ, and γ, we can simulate the population dynamics of wolves and rabbits over a specific time frame. Additionally, setting appropriate initial values for the populations of wolves and rabbits is crucial to accurately reflect their starting conditions in the model.