As a general rule, MATLAB is a scientific software whose main goal is the efficient implementation of numerical approximation algorithms, while MAPLE and MATHEMATICA were originally developed to perform symbolic computation only. They presently include also implementations of numerical algorithms and can also be used for computing numerical approximations, but (warning: opinion a MATLAB user!) I think it is fair to say that the range of numerical algorithms available in MATLAB and the level of optimization it achieves is probably superior. On the other hand, a complete and fair comparison is probably difficult to carry out and perhaps meaningless, since, as stated in the beginning, the main goals of these two kinds of tools are different. This is reflected in the two rather different user communities associated to these software families: developers of numerical methods mostly use MATLAB (or other numerical approximation packages) while researchers in mathematical analysis, geometry, mathematical physics who must carry out complex symbolic computation often use MAPLE, MATHEMATICA (or other similar packages).

It is also important to mention several other non proprietary environments available for these purposes (Scilab, Octave, Python for example).

how do we implement the code in matlab for presenting phase diagram in prey -predator model