Abstract
The dynamics of memristor-based RLC circuit is explored on the effects of magnetic field coupling through a transformer in the circuit. With the increasing strength of magnetic field coupling, the two coupled RLC circuits firstly break the reflectional symmetry by transiting from double-scroll attractors to single-scroll attractors and then break the translational symmetry with two attractors in different sizes and shapes. The two single-scroll attractors are locked in antiphase synchronous states for positive magnetic field coupling while transit to a new kind of dynamic regime, named as central symmetrical antiphase synchronization (CSAS) for negative magnetic field coupling. Moreover, the single-scroll attractors in inphase synchronization or in CSAS may coexist with asynchronous states in some interval of coupling strength. The dynamics of the anti-synchronization and the CSAS of the coupled memristor-based circuits have potential applications in nonvolatile memories, neuromorphic devices to simulate learning, adaptive and spontaneous behaviors.
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