Quasilinear approach to nonlinear systems and the design of n-double scroll (n = 1, 2, 3, 4,ellipsis (horizontal))

The double scroll is a strange attractor showing unpredictable transitions from one scroll to another. In the paper, an attractor is constructed that consists of n scrolls (n may be chosen). This was made possible by the development of an alternative method for studying nonlinear differential equations, called a quasilinear approach. The method is very qualitative, but it gives a global insight into the behaviour of the dynamical system and it may be used as a complement to a linearisation around equilibrium points or a Lyapunov function method.