Parameter converting method for bifurcation analysis of nonlinear dynamical systems

For detecting behavior of a dynamical system, bifurcation analysis is necessary with respect to change in parameters of system. In this work, based on the solution of ordinary differential equations from initial value and parameters, a simple method is presented, which can efficiently reveal different bifurcations of system. In addition to its simplicity, this method does not required to have deep physical and mathematical understanding of the problem, and because of its high precision and the speed of solutions, does not need to reduce the order of models in many complex problems or problems with high degrees of freedom. This method is named parameter converting method (PCM), which has two steps. In the first step the parameter is varied as a function of time and in the second step, time is expressed as inverse of this assumed function. With this method bifurcation and amplitude-frequency diagrams and hidden attractors of some complex dynamics will be analyzed and the sensitivity of the multi potential well systems to initial conditions is studied. With this algorithm, a simple way to find the domain of high-energy orbit in bistable systems is obtained.