Multi-scroll Chaotic Oscillator Based on a First-Order Delay Differential Equation

Abstract

After the discovery of the well-known chaotic Lorenz’s system, the study of chaos has received considerable attention due to its promising applications in a variety of fields, ranging from physics, economics, biology to engineering. Moreover, chaotic systems with multiple scrolls can exhibit more rich dynamics than the general chaotic ones with few attractors. This expansion of dynamics leads to multi-scroll chaotic oscillators showing better performance in several chaotic-based applications, such as secure communication, encrypting fingerprint image, controlling motion directions of autonomous mobile robots, or generating pseudo random numbers etc. As a result, investigating new chaotic oscillators with multiple scrolls has been become an attractive research direction of both theoretical and practical interest recently. Although numerous approaches for constructing multi-scroll attractors from conventional three-dimension chaotic systems have been reported intensively, there are few publications regarding the multi-scroll attractors from infinite dimensional time-delay systems. This work presents a new multi-scroll chaotic oscillator and its circuital design. This chaotic system is described by a first-order delay differential equation with piecewise linear function. It is shown through simulations that the proposed system can exhibit odd number of scrolls of chaotic attractors such as three-, five-, seven-, and nine-scroll attractors. In addition, the detailed implementation of the proposed multi-scroll oscillator using the electronic simulation package Multisim is also presented to show the feasibility of the oscillator. The Multisim results of the chaotic oscillator are well agree with the numerical simulation results. It is noting that the new multi-scroll chaotic circuit has been designed with simple common components, like resistors, capacitors, and operational amplifiers.