All of this is described in the MATLAB documentation: http://www.mathworks.nl/help/techdoc/ref/matlabunix.html .
-nodisplay: Launch the Sun Microsystems JVM software, but do not start the MATLAB desktop. Do not display X commands and ignore DISPLAY environment variable,
-nodesktop: start MATLAB without creating the MATLAB desktop. The JVM software starts. Use the current window in the operating system to enter commands. Use this option to start without an X window, for example, in VT100 mode or in batch processing mode. Note that if you connect to MATLAB using the> constructor, the nodektop option is used automatically. With nodektop, MATLAB does not save instructions in Command History. With nodektop, you can still use most of the development environment tools by running them through a function. For example, use preferences to open the Preferences dialog box and a document to open the help browser. Do not use nodektop to create a command window interface only; instead, choose Desktop> Desktop Layout> Command Window Only.
-nojvm: Run MATLAB without the JVM software. Use the current window to enter commands. MATLAB desktop does not open. Any tools that require Java software, such as desktop tools, cannot be used. Handle graphics and related functionality are not supported; MATLAB issues a warning when you use them.
-nosplash: launches MATLAB, but does not display a splash screen at startup.
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