A multistage linearisation approach to a four-dimensional hyperchaotic system with cubic nonlinearity

This paper reports on a new multistage extension of the successive linearisation method to a four-dimensional chaotic system that generates various complex attractors for different parameter values. The solutions are found by subdividing the domain into several intervals in which the linearisation method is used to find approximate solutions that are then matched across all the intervals. The solutions and phase portraits for the cyclic and chaotic cases are given. Finally we compare this approach to the Runge–Kutta based ode45 solver and other results in the literature to show that the multistage linearisation method gives accurate results.