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Generating self-excited and hidden attractors with complex dynamics in a memristor-based Jerk system

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In this paper, we report a special memristor-based Jerk system in which self-excited and hidden attractors can be generated by adjusting one decisive system parameter. With increasing the parameter from negative to positive, the system has a transition from unstable equilibriums to no equilibrium point, and thus leading to the occurrence of coexisting self-excited and hidden attractors in the modified Jerk system simultaneously. More interestingly, the memristor parameters play an important role in the coexistence of attractors and the formation of the Feigenbaum remerging trees, and these two dynamic behaviors can be found in both hidden and self-excited attractor regions. In addition, the study of state-switching proves that the memristor’s internal initial state is very sensitive to the system. In order to verify the complex dynamic behavior of the system, an analog circuit simulation based on Multisim is developed and two types of attractors and their coexisting attractors are successfully captured.

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Thanks to the National Key Research and Development Program of China (Grant Nos. 2018AAA0103300) and National Natural Science Foundation of China (Grant Nos. 62071411) for supporting this work.

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Correspondence to Zhijun Li.

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Zeng, D., Li, Z., Ma, M. et al. Generating self-excited and hidden attractors with complex dynamics in a memristor-based Jerk system. Indian J Phys 97, 187–201 (2023).

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