Abstract
The main aim of this work is to generalize the chaotic unified model using the quaternion mathematics and fractional derivatives. A novel 8.1-fractional order, 9-dimensions, quaternion unified chaotic system is constructed. The 8.1-fractional order electronic circuit that realize the novel system is designed. Using the graph theory tools, the complexity of the proposed novel 8.1-fractional order, 9-dimensions, quaternion unified chaotic system is calculated. In addition, the substantial contribution in this work appears in introducing an extraordinary type of quaternion synchronizations. We call this novel type "quaternion anti synchronization"(QAS). QAS has unusual properties and characteristics that distinguish it from all the types of synchronizations previously studied in the literature. The QAS of fractional unified model with quaternion variables is studied. The validity of the analytical results is confirmed in QAS of fractional unified system with effective numerical simulation.
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