The PATH program for the pathfollowing of the solutions of the nonlinear equations

During the analysis of the mathematical models in physics, chemistry, biology, medicine, ecology there arises a necessity for the pathfollowing of the solutions of the nonlinear equations. To help those researchers who have come into the collision with that necessity, the authors are developing the computer program called PATH, which is devoted, in particular, to the pathfollowing of the stationary and periodic solutions of the systems of the ordinary autonomous differential equations.
This article describes the pathfollowing problems the PATH program is capable to solve. The example of the application of the program to the analysis of the mathematical model of the catalytic reaction (CO+O$_2$)/Pd(110) is observed as well. Using the PATH program there has been calculated the map of bifurcations of the stationary solutions of the system of the ordinary autonomous differential equations the model is based upon, and the dependence of the map of bifurcations on the parameters has been studied.