In this lab, the dynamics of prey-predator relationship is mathematically studied using Lotka−Volterra equations. Here the rat (prey) and snake (predator) is taken as an example to study the prey-predator cycle. The steps for working out the simulator are discussed in the following sections.

 

1. While clicking the “Simulator “tab one will get a page as shown below.

 

 

2. The “variables’ in the simulator window are default values. User can change the values according to the data to be tested.
    

 

The Variable Menu consists of

                                                          

 

 The 'Initial rat population' tab can be used to enter initial population number or count of the rat (prey) population being studied. Also the 'Initial snake population' tab can be used to enter the starting or initial population number or count of the snake (predator) population being studied.

 

                                                                     

 

The 'Number of steps' tab provides the user the option to run the simulator in as many steps.  The 'Step size' tab provides the user to reduce the number of steps given in the tab “Number of steps” in terms of the step size given in this tab, for example say if number of step is 10 and the step size is 10 then the simulation could be over in just one step, if the step size is given as 1. For the same number of steps as in previous case if the step size was given as 1 then simulation would have finished in 10 steps only.

 

                                                                    

 

Tools for 'Simulation Control:

 

 

 

Table 1 shows the importance of each tab in the Simulation Control Menu

 

 

Table 1: Simulation Control Parameters

 

Viewable Window in the Simulator

 

Table 2 shows the importance of each tab in theViewable Window in the simulator

 

  Table 2: Parameters in the Viewable window of the Simulator

 

 

Sample Problem:

 

• Consider an example, where the initial prey population is 1000, and initial predator population 100. Let us take the number of steps and step size as 100 and 10 respectively. Let us find out the dynamics of prey predator population over a specific time period.

 

                            To find this, one should apply the provided parameters in the specific boxes in the simulation tab.

 

[Initial prey population = 1000,  Initial predator population = 100,  Number of steps = 100,  Step size = 10]

 

 

 

When the Iteration is completed click on the data plots tab to view the prey-predator cycle for the assumed values.

 

 

The graph will be displayed on the Simulators Viewable window.

 

 

On the peak of each plot, the population of rats and snakes at that specific period  is displayed.

 

 

On clicking the “Statistics” tabs, the population of rats and population of snakes for the assumed values are displayed on the simulator window

 

         

 

Result Interpretation:

 

The population of prey and predators are calculated using the mathematically modeled simulator of Lotka-Volterra Prey-Predator equation. In this example, the population of rats and Population of Snakes are calculated as 5675.204 and 31.565 for the given parameters.