Memristor-based Gauss chaotic maps with hidden/self-exited dynamics

References

• M.-S. Abdelouahab, R. Lozi and L. Chua, Memfractance: a mathematical paradigm for circuit elements with memory, Int. J. Bifurc. Chaos 24 (2014), p. 1430023.
   Web of Science ®Google Scholar
• A. Algaba, F. Fernández-Sánchez, M. Merino and A.J. Rodríguez-Luis, Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system, Chaos 23 (2013), p. 033108
   PubMed Web of Science ®Google Scholar
• A. Algaba, F. Fernández-Sánchez, M. Merino and A.J. Rodríguez-Luis, The Lü system is a particular case of the Lorenz system, Phys. Lett. A 377 (2013), pp. 2771–2776.
   Web of Science ®Google Scholar
• B. Bao, K. Rong, H. Li, K. Li, Z. Hua, and X. Zhang, Memristor-coupled logistic hyperchaotic map, IEEE Trans. Circ. Syst. II Exp. Briefs 68 (2021), pp. 2992–2996.
   Web of Science ®Google Scholar
• H. Bao, C. Chen, Y. Hu, M. Chen and B. Bao, 2-D piecewise linear neuron model, IEEE Trans. Circ. Syst. II., Exp. Briefs 68 (2021), pp. 1453–1457.
   Web of Science ®Google Scholar
• H. Bao, Z. Hua, H. Li, M. Chen and B. Bao, Discrete memristor hyperchaotic maps, IEEE Trans. Circ. Syst. I Reg. Papers 68 (2021), pp. 4534–4544.
   Web of Science ®Google Scholar
• H. Bao, Z. Hua, H. Li, M. Chen and B. Bao, Memristor-based hyperchaotic maps and application in AC-GANs, IEEE Trans. Ind. Inform. (2021), doi:10.1109/TII.2021.3119387.
   Web of Science ®Google Scholar
• H. Bao, Z. Hua, N. Wang, L. Zhu, M. Chen and B. Bao, Initials-boosted coexisting chaos in a 2-D Sine map and its hardware implementation, IEEE Trans. Ind. Inform. 17 (2021), pp. 1132–1140.
   Web of Science ®Google Scholar
• V. Botella-Soler, J.M. Castelo, J.A. Oteo and J. Ros, Bifurcations in the Lozi map, J. Phys. A: Math. Theor. 44 (2011), p. 305101.
   Web of Science ®Google Scholar
• Y. Deng and Y. Li, Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map, Nonlinear Dyn. 104 (2021), pp. 4601–4614.
   Web of Science ®Google Scholar
• R.L. Devaney, Fractal patterns arising in chaotic dynamical systems, in The Science of Fractal Images, H.O. Peitgen and D. Saupe, eds., Springer, New York, 1988, pp. 137–168.
   Google Scholar
• C. Dong, K. Sun, S. He and H. Wang, A hyperchaotic cycloid map with attractor topology sensitive to system parameters, Chaos 31 (2021), p. 083132
   PubMed Web of Science ®Google Scholar
• D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznetsov, G.A. Leonov and A. Prasad, Hidden attractors in dynamical systems, Phys. Rep. 637 (2016), pp. 1–50.
   Web of Science ®Google Scholar
• M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys. 50 (1976), pp. 69–77.
   Web of Science ®Google Scholar
• R.C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford Univ. Press, New York, 2004
   Google Scholar
• Z. Hua, Y. Zhou and B. Bao, Two-dimensional sine chaotification system with hardware implementation, IEEE Trans. Ind. Informat. 16 (2020), pp. 887–897.
   Web of Science ®Google Scholar
• Z. Hua, Y. Zhou, C.M. Pun and C.L.P. Chen, 2D sine logistic modulation map for image encryption, Inform. Sci. 297 (2015), pp. 80–94.
   Web of Science ®Google Scholar
• S. Jafari, V-T. Pham, S.M.R.H. Golpayegani, M. Moghtadaei and S.T. Kingni, The relationship between chaotic maps and some chaotic systems with hidden attractors, Int. J. Bifurc. Chaos 26 (2016), p. 1650211.
   Web of Science ®Google Scholar
• H. Jiang, Y. Liu, Z. Wei and L. Zhang, Hidden chaotic attractors in a class of two-dimensional maps, Nonlinear Dyn. 85 (2016), pp. 2719–2727.
   Web of Science ®Google Scholar
• H. Jiang, Y. Liu, Z. Wei and L. Zhang, A new class of two-dimensional chaotic maps with closed curve fixed points, Int. J. Bifurc. Chaos 29 (2019), p. 1950094.
   Web of Science ®Google Scholar
• A.-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, R. Lozi and V.-T Pham, On fractional-order discrete-time systems: Chaos, stabilization and synchronization, Chaos Solitons Fractals 119 (2019), pp.150–162.
   Web of Science ®Google Scholar
• A.A. Khennaoui, A. Ouannas, S. Boulaaras, V.-T. Pham and A.T. Azar, A fractional map with hidden attractors: Chaos and control, Eur. Phys. J. Spec. Top. 229 (2020), pp. 1083–1093.
   Web of Science ®Google Scholar
• H. Li, Z. Hua, H. Bao, L. Zhu, M. Chen and B. Bao, Two-dimensional memristive hyperchaotic maps and application in secure communication, IEEE Trans. Ind. Electron. 68 (2021), pp. 9931–9940.
   Web of Science ®Google Scholar
• H. Li, K. Li, M. Chen and B. Bao, Coexisting infinite orbits in an area-preserving Lozi map, Entropy 22 (2020), p. 101119.
   Web of Science ®Google Scholar
• K. Li, H. Bao, H. Li, J. Ma, Z. Hua and B. Bao, Memristive Rulkov neuron model with magnetic induction effects, IEEE Trans. Ind. Inform. 18 (2022), pp. 1726–1736.
   Web of Science ®Google Scholar
• M. Liu, S. Zhang, Z. Fan, S. Zheng and W. Sheng, Exponential H1 synchronization and state estimation for chaotic systems via a unified model, IEEE Trans. Neural Netw. Learn. Syst. 24 (2013), pp. 1114–1126.
   PubMed Web of Science ®Google Scholar
• R. Lozi, Un attracteur étrange du type attracteur de Hénon, J. Phys. 39 (1978), pp. 9–10.
   Google Scholar
• Y. Ma, C. Li and B. Ou, Cryptanalysis of an image block encryption algorithm based on chaotic maps, J. Inf. Secur. Appl. 54 (2020), p. 102566.
   Web of Science ®Google Scholar
• H. Natiq, S. Banerjee, M.R.K. Ariffin and M.R.M. Said, Can hyperchaotic maps with high complexity produce multistability?, Chaos 29 (2019), p. 011103.
   PubMed Web of Science ®Google Scholar
• S. Panahi, J. Sprott and S. Jafari, Two simplest quadratic chaotic maps without equilibrium, Int. J. Bifurc. Chaos 28 (2018), p. 1850144.
   Web of Science ®Google Scholar
• Ο.Ε. Rössler, An equation for continuous chaos, Phys Lett A 57 (1976), pp. 397–398.
   Web of Science ®Google Scholar
• J.C. Sprott, Simple chaotic systems and circuits, Am. J. Phys. 68 (2000), pp. 758–763.
   Web of Science ®Google Scholar
• W. Tucker, The Lorenz attractor exists, C. R. Acad. Sci. Paris, Ser. I Math. 328 (1999), pp. 1197–1202.
   Google Scholar
• C.F. Wang and Q. Ding, A new two-dimensional map with hidden attractors, Entropy 20 (2018), p. 322.
   PubMed Web of Science ®Google Scholar
• N. Wang, G.S. Zhang, N.V. Kuznetsov and H. Bao., Hidden attractors and multistability in a modified Chua’s circuit, Commun. Nonlinear Sci. Numer. Simul. 92 (2021), p.105494.
   Web of Science ®Google Scholar
• Y. Xiao, K. Sun, M. Yu and X. Xu, Dynamics of a new multi-cavity hyperchaotic map and its DSP implementation, Int. J. Bifurc. Chaos 29 (2019), p. 1950194.
   Web of Science ®Google Scholar
• X. Zhang and G.R. Chen, Polynomial maps with hidden complex dynamics, Disc. Contin. Dyn. Syst. Ser. B. 24 (2019), pp. 2941–2954.
   Web of Science ®Google Scholar
• J. Zhao, Complexity and chaos control in a discrete-time Lotka-Volterra predator-prey system,J. Differ. Equ. Appl. 26 (2020), pp. 1303–1320.
   Web of Science ®Google Scholar
• J. Zhong, L. Zhang and G. Tigan, Bifurcations of a discrete-time neuron model, J. Differ. Equ. Appl. 23 (2017), pp. 1508–1528.
   Web of Science ®Google Scholar