Third-Order Autonomous ODE with Slider Controllable Parameters and Inputs (version 1.4)

This page/program is an augmentation of the 3rd-order ODE tool:
          dy0/dt=f0(y0,y1,y2,t)=F0(y0,y1,y2,A,B,C)+K0*u(t),
          dy1/dt=f1(y0,y1,y2,t)=F1(y0,y1,y2,A,B,C)+K1*u(t),
          dy2/dt=f2(y0,y1,y2,t)=F2(y0,y1,y2,A,B,C)+K2*u(t),
          at t=0, y0(t)=y0(0), y1(t)=y1(0), y2(t)=y2(0).

In math equation style:
`dy_0/dt=f_0(y_0,y_1,y_2,t)=F_0(y_0,y_1,y_2,A,B,C)+K_0*u(t),`
`dy_1/dt=f_1(y_0,y_1,y_2,t)=F_1(y_0,y_1,y_2,A,B,C)+K_1*u(t),`
`dy_2/dt=f_2(y_0,y_1,y_2,t)=F_2(y_0,y_1,y_2,A,B,C)+K_2*u(t),`
at `t=0, y_0(t)=y_0(0), y_1(t)=y_1(0), y_2(t)=y_2(0).`

That is, you can insert 1 to 3 Slider Controllable parameters, A, B, and/or C, into the Fi() function definitions, 
to easily explore the characteristics of the ODE, which are affected by changes of A, B, and/or C parameters. 

When you open this page, the solution/simulation of a default/pre-defined example ODE is ready to run.

For "Solve" started solution:
Click "Solve" button to display the solution for the ODE over a time period: [0, T], where T=N*dT.
Move the sliders to change the value of the A, B, and/or C parameters.
Click "Solve" button again to display the new solution and observe the changes of the graphs.

For "Start/Reset" started solution:
Click "Start/Reset" button to run the ODE simulation continuously.
Move the sliders to change the value of the A, B, and/or C parameters.
The running solution/simulation will be affected by the controllable parameters in real-time.

This tool is useful for exploring periodic or chaotic characteristics of the ODE, which are affected by changes of A, B, and/or C parameters. 

The default example is a Lorenz system. Its 3 parameters are multiplied by A, B, and C, respectively.
It can be observed that changes of the parameters will affect the chaotic characteristics of the Lorenz system, or make it a periodic system, or make it converge to a point, or cause it unstable.

You can define your own ODE function, and put variables: A, B, and/or C, in to your function formula.
Re-define A, B, and/or C range (max and min), if needed.
You can also put A, B, and/or C variables into the selectable ODE examples.

For more detailed usage Information, see the Third Order ODE tool.

Restart/Reload This Web Page

Use Checkboxes to Select Variables to Display(Must at Least Select 1 Variable):
y0(t): y1(t):y2(t):u(t):.

Menu to Select 2 Variables for the Phase Plane Plotter:
Keep Graph Shape or Not:

Push "Start" or "Solve" Button to Run the Predefined Example

If Change A, B or C Slider Range(Max and/or Min), Press "Enter" Key or Click Outside the Text Box:

A Min:........................A Max:

A: 1.0

B Min:........................B Max:

B: 1.456

C Min:........................C Max:

C: 1.234

Set Time Step-Size dT(sec) and Number of Data to Display N:

dT:N:

Set Initial Value y0(0), y1(0), and y2(0):

y0(0):y1(0):y2(0):

Input Your Own Functions: F0(y0,y1,y2), F1(y0,y1,y2), F2(y0,y1,y2) or Use the Example Functions:

F0(y0,y1,y2):

F1(y0,y1,y2):

F2(y0,y1,y2):

Menu to Select an Input Signal U(t):
U(t):

Set Input Signal Period Ts(sec), Amplitude Am, and K0, K1, K2:

Ts:Am:K0:K1:K2:

Saved Projects:

How to save your projects for later use:
Click "Save Project" to save the current project to your device. All necessary function(s) and parameters will be saved.
Click "Load Project" to load a saved project and run it.
Click "Delete Project" to remove the selected project from your device.
Note: Your projects will remain saved to your device unless you delete them or you clear the site data of your browser.

Sharing your projects:
To create a URL link for the current project, click the "Share Function" button below the graph(s).
This will copy a link containing the current project to your clipboard that you can share with others.
You can also save a PNG image of the current graph by clicking the "Save Graph as Image" button.

Disclaimer: No data saved with these tools are kept by or sent to mathonthecloud.com. Everything is saved locally to your device only.