# Fibonacci with discrete time models

We used the **gvle.discrete-time** package to model the Fibonacci sequence into the discrete-time extension
(package vle.discrete-time)

Video comments:

- 0:00 : Create the package
*fibonacci*and specify a dependency to the vle.discrete-time package. - 0:18 : Create a new atomic model based on the discrete time formalism.
By default, its name is
*NewCpp*. - 0:25 : Specify the equation
*F= F(-1) + F(-2)*into the*Compute*section. - 0:35 : Declare the variable
*F*and the set an history size of 2. - 0:45 : Set initial history
*F{n=-1}=0*and*F{n=0}=1*. - 0:58 : Rename the atomic model to
*Fibonacci*, configure and build the project. - 1:19 : Open the default model
*empty.vpz*and add an atomic model, configure it with the newly created dynamic*Fibonacci*from package*fibonacci*. - 1:29 : Into the
*Observables*tab, attach the observable port*F*to the available view of the*vpz*. - 1:38 : Into the
*Project*tab, specify the duration of the simulation to 6. - 1:48 : Into the
*Simulation*tab, launch simulation and select the variable*F*for plotting.

# Lotka Volterra equation with Forrester diagrams

We used the **gvle.forrester** package to model the Lotka Volterra equations into the Ordinary
Differential Equations (package vle.ode)

Video Comments:

- 0:00 : Create the package
*lotkavolterra*and specify a dependency to the vle.ode package. - 0:18 : Create a new atomic model based on the Forrester formalism.
By default, its name is
*NewCpp*. - 0:24 : Define two compartments
*x*and*y*and give their initial values. - 0:46 : Define four parameters
*alpha*,*beta*,*gamma*and*delta*and give their values. - 1:36 : Define two material flows
*flowX*and*flowY*. - 1:53 : Declare a hard link from flows to compartments.
- 1:59 : Declare dependencies between flows and parameters.
- 2:23 : Give equations of the flows (depending on compartments and parameters).
- 3:06 : Modify the time step to 0.01, for the Euler method, of the numerical integration.
- 3:22 : Close the atomic model description and rename it to
*LotkaVolterra*. - 3:24 : Configure and build the project.
- 3:44 : Open the default model
*empty.vpz*and add an atomic model, configure it with the newly created dynamic*LotkaVolterra*from package*lotkavolterra*. - 3:56 : Into the
*Observables*tab, attach the observable ports to the available view of the*vpz*. - 4:11 : Save file and select the
*Simulation*tab to launch simulation. - 4:18 : Change the duration of simulation, re-launch simulation, and plot the
compartments
*x*and*y*.

# Old VLE 1.1 tutorials

These tutorials are made for the version 1.1 of VLE.

## First model

- First models: create two models from scratch and assign observation. Keywords: C++, package and observation.

## Lotka-Volterra

- Lotka-Volterra: create a simple Euler model, assign observation and experiment conditions. Keywords: C++, package, observation, conditions and RVLE.

## Forrester

This tutorial shows how to use the Forrester extension:

- See System Dynamics to get the basic concepts.
- The example in this tutorial consists in modeling the Lotka Volterra equations.