sentences:  Parameter continuation also gives a more dependable system to analyze a dynamical system as it is more stable than more interactive, time-stepped numerical solutions.Especially in cases where the dynamical system is prone to blow-up at certain parameter values (or combination of values for multiple parameters).It is extremely insightful as to the presence of stable solutions (attracting or repelling) in the study of Nonlinear Partial Differential Equations where times stepping in the form of the Crank Nicolson algorithm is extremely time consuming as well as unstable in cases of nonlinear growth of the dependent variables in the system.