Investigation of Dynamical Systems with XPPAUT

Abstract

The mathematical modeling and computer simulations are extensively used in engineering problems and scientific research. The analysis of the system model gives us idea of understanding of the system whereas the simulation explains the feasibility whether system is implementable or not. Simulation also gives insight of the system realization. This paper focuses on interactive computational and simulation software XPPAUT (X-Windows Phase Plane Auto). Many Softwares i.e. MATLAB, MATHEMATICA, MAPLE are currently used for modeling and simulations of dynamical systems, but numerically integrating the differential equations is slower than that can be achieved with XPPAUT. Some problems incorporating the well-known linear and non-linear differential equations i-e radioactive decay, simple pendulum, Lorenz system, initial value problems and direction fields along-with null-clines has been coded, simulated and the results are presented to substantiate the claim.