A new four-scroll chaotic attractor and its engineering applications

In this paper we investigate a new system of three coupled nonlinear ordinary differential equations, whose dynamics support periodic and chaotic attractors as certain parameters vary. In its most general form, the system has nine parameters. However we can set up to three of these parameters to zero, and still obtain complex dynamics. Here we discuss the case where only two of these parameters are set to zero, and present two-parameter bifurcation linear stability curves for various combinations of the remaining parameters. Then we compute Lyapunov exponents, to verify the regimes of chaotic dynamics, and use adaptive control theory to influence the behaviour. An electronic circuit model of the new chaotic system has been designed and its simulations have been performed using an ORCAD-PSpice program. An experimental realisation of the new chaotic circuit has been carried out and oscilloscope outputs have been compared with numerical (digital) and electronic circuit simulation results. We then used the chaotic system to design a random number generator, and show that the new system has the potential of being used in several scientific and engineering fields such as communication, image processing, physics and mechatronics.