Please solve using Wolfram Mathematica

This problem will build on the skills you've learned so far in the course and in the previous problems to create a simulation of the dynamics of the cell cycle model described in this chapter and in Chapter 5. The goal is to use Manipulate to show the vector field, the nullclines, and the equilibrium points of the system as you vary a single control parameter, the cell size m. Much of the code that you need to do this is already available in Chapter 6. Some of it will need to be modified. The parts of the question will guide you through the steps necessary to reach the final goal of a working dynamic model.

a. Creating a dynamic view of the vector field: Ordinarily, we encourage you to put every command in a separate cell. Even as you work on this question, you are encouraged to initially put commands in separate cells, evaluate them, and see that they work.

However, once you are putting together a complex model, and have checked that the individual commands work, it is often useful to group the commands together. This makes it less likely that if you copy and modify the code, you leave a command behind. It also makes the model more compact.

The key to combining statements in a cell is the use of the CompoundExpression symbol, the semicolon (;). If you put two commands in the same cell without this, then Mathematica may think you are trying to multiply the two commands, and the results will be confusing and frustrating. If you put semi-colons between the commands, Mathematica evaluates each statement in turn, and only provides output for the final statement.

In general, for many of the models that you will build, it will be useful to have an initialization cell, which contains parameters, function definitions, and other material that you want to evaluate before you run your model. You can group all of these commands in a single cell as long as they are separated by semicolons. It is also an excellent idea to add comments, using the delimiters (* and *). This internal documentation clarifies what each command does, and greatly speeds up debugging.

Then, you may want a separate cell for the commands that actually run the model. This design often makes it easier to debug a complicated model.

Here are the specific instructions you need to start building the model for this part of the question:

Copy the definitions of the xcoord and ycoord from section 6.3 of the chapter into a single cell in your own notebook, separating them with a semicolon (;). This provides you with the definitions you need in your initialization cell.

In a separate cell (for running the model), create a Manipulate function. Within Manipulate, copy the definition of gfullsystem from section 6.3, and replace the 0.3 with a new variable, mvalue, which will be the variable that you manipulate. In the command section for Manipulate, give mvalue the default value of 0.3, the name "Cell Size", and the range 0 to 1.

In order to ensure that the model works, make sure that you evaluate the cell containing the commands that initialize the key variables outside of the Manipulate function, as well as evaluating the cell containing the Manipulate function. In general, you will need to be sure you evaluate any initialization commands outside of Manipulate for any model that you build in this way using Manipulate. Confirm that when you evaluate the model with the given parameters, you obtain Figure 6.3.1.

Test that your model is working by moving the slider and varying the value of m from 0 to 1. What do you observe happening to the vector field, and what does this imply about the cell's state relative to the "Start" and "Finish" checkpoints?