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Memristive Hénon map with hidden Neimark–Sacker bifurcations

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Abstract

Due to the nonlinearity with inner state, memristors have been applied in vast continuous dynamical systems. However, the application of memristors in discrete dynamical systems has not received enough attention, yet. Toward this end, this paper presents a three-dimensional (3D) memristive Hénon map by coupling a memristor to the classical Hénon map. Using numerical measures, the memristor effects on the presented map are exhibited and the complex dynamical behaviors with multistability are disclosed therein. Particularly, since the presented map has no invariant points, a dimension-reduction conversion method is proposed to investigate its properties and its hidden Neimark–Sacker bifurcations are effectively interpreted. The results demonstrate that the introduction of discrete memristor makes the presented map own complex hidden dynamical behaviors, which greatly enhances the fractal structure complexity of the chaotic attractors. In addition, a digital hardware set is exploited to implement the 3D memristive Hénon map and the chaotic attractors are physically acquired thereby.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundations of China under Grant Nos. 51777016 and 62071142 and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China, under Grant No. KYCX21_2816.

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Correspondence to Bocheng Bao.

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Rong, K., Bao, H., Li, H. et al. Memristive Hénon map with hidden Neimark–Sacker bifurcations. Nonlinear Dyn 108, 4459–4470 (2022). https://doi.org/10.1007/s11071-022-07380-z

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