The Design And Hardware Realization Of A Family Of A Novel Chaotic Circuits

Researching and observing chaotic phenomenon began with early 1980s bycomputer simulation and circuit experiment. Over the last two decades, there are alarge number of relative results in this field, especially in the realization of multi-scrollchaotic attractors. The design and hardware realization of a family of a novel chaoticcircuits have been studied in the paper.High-order Jerk systems are a family of a novel chaotic systems which were foundin 2006 based on third-order Jerk system. There is no relative literature about theircircuit design. This paper proposes a general high-order Jerk circuit which can realizefourth-order and fifth-order Jerk circuit via the control of switches. Some numericalsimulation results and experimental results are showed in the paper.High-order Jerk systems only generate one- or tow-scroll chaotic attractoraccording the literature, cannot generate multi-scroll chaotic attractors. A approach forgenerating multi-scroll chaotic attractors in fourth-order and fifth-order Jerk systems isproposed via constructing step function series. According to the theory of generatingmulti-scroll chaotic attractors via step function series, a novel circuit is designed forexperimental verification of multi-scroll chaotic attractors. The prominent feature forthis kind of circuit design method is self-unified and in a sense universal. Based on theuniform circuit, both for fourth-order and fifth-order general Jerk circuits can berealized with the switching control. The switches set are also used to control thenumber of scrolls. Finally, the computer simulations and hardware implementations aregiven on the fourth-order and fifth-order general Jerk circuits to generate multi-scrollchaotic attractors.An approach for generating multi-directional grid chaotic attractors from athird-order autonomous system is proposed via constructing a series of step functions,including two-directional and three-directional multi-scroll chaotic attractors. Circuitsare designed based on the hardware circuit platform. Some numerical simulation and experimental results are showed, such as 2-D 2×2,3×2,4×4-grid scroll and 3-D2×2×2,3×3×3-grid scroll. It has been verified that numerical simulation results aresame as experimental results.This paper mainly has two innovations. The first is that a approach for generatingmulti-scroll chaotic attractors in fourth-order and filth-order Jerk systems is proposedvia constructing step function series, and a circuit is designed for hardware experiment.The second is that a approach for generating multi-directional grid chaotic attractors ina third-order system is proposed via constructing some non-liner function, and circuitsare designed for hardware experiment.