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A nanoscale memristor can replace the nonlinear part of a chaotic system, which can greatly reduce the physical size of the chaotic system. More importantly, it can enhance the complexity of the chaotic system and the randomness of signals. In this paper, a new memristor-based chaotic system is designed based on a new three-dimensional autonomous chaotic system. In order to study the complex dynamic characteristics of the memristive system, the chaotic system is investigated by the theoretical derivation, numerical simulation, stabilization of equilibrium points, and Lyapunov exponent spectrum. The influences of different parameters on the phase diagram and the stability of equilibrium point of this system are also discussed in detail. It is interesting that when system parameters a and c take different values, the location and stability of the equilibrium point of the system will be changed, then two scrolls of the system will be overturned at a different angle, and it will produce a different degree of aliasing between the two scrolls. Parameter b has a large variable range, when it is changed, and the system will transform into three kinds of classical chaotic systems defined by Vaněček and Celikovsk. These indicate that the memristor-based chaotic system has a lot of valuable dynamic behaviors, so it has applications in the field of secure communication, information processing etc. Field programmable gate array (FPGA) technology has a large capacity and high reliability, which is widely used in modern digital signal processing. And with the development of FPGA technology, applying FPGA technology to realizing the chaotic systems has gradually become a hot topic. Moreover, the improved Newton iteration method is used to design a square root operator of memristor in this paper by using verilog hardware description language (verilog HDL) which only needs three times iteration to reach the required accuracy. The results of FPGA hardware are consistent with the numerical simulation results. It breaks through the previous bottleneck that the chaotic system based on titanium dioxide memristor can only be simulated in computer, which is of great significance for further studing of memristor, and provides a reference for further research on the memristor-based chaotic system and applications in secure communication and information processing.
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Keywords:
- new chaotic system /
- memristor /
- dynamical behavior /
- field programmable gate array
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chua L O 1971 IEEE Trans. Circ. Theor. 18 507
[3] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4] Kavehei O, Iqbal A, Kim Y S, Eshraghian K, Al-Sarawi S F, Abbott D 2010 Proc. R. Soc. A 466 2175
[5] Biolek Z, Biolek D, Biolkov V 2009 Radio. Eng. 18 210
[6] Pershin Y V, Di V M 2008 Phys. Rev. B 78 3309
[7] Jo S H, Kim K H, Lu W 2009 Nano Lett. 9 870
[8] Yang J, Wang L D, Duan S K 2016 Sci. China Inf. Sci. 46 391
[9] Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2015 Neurocomputing 171 23
[10] Wang L D, Duan M T, Duan S K, Hu X F 2014 Sci. China Inf. Sci. 44 920
[11] Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364
[12] Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 417
[13] Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205
[14] Zhong G Q, Man K F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 2907
[15] Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 54 2180
[16] Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[17] Min G Q, Wang L D, Duan S K 2015 Acta Phys. Sin. 64 210507 (in Chinese) [闵国旗, 王丽丹, 段书凯 2015 64 210507]
[18] Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 7
[19] Wang L D, Duan S K 2012 Abstr. Appl. Anal. 2012 2012
[20] Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 61 110502]
[21] Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[22] Wang Z L 2008 Comput. Eng. Appl. 44 84 (in Chinese) [王忠林 2008 计算机工程与应用 44 84]
[23] Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 63 060501]
[24] Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xi'an Electronic Sience and Technology University Press) pp126-148 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第126-148页]
[25] Vaněčk A, Člikovsk S 1996 Control Systems: From Linear Analysis to Synthesis of Chaos (London: Prentice Hall International Ltd.) pp10-121
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chua L O 1971 IEEE Trans. Circ. Theor. 18 507
[3] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4] Kavehei O, Iqbal A, Kim Y S, Eshraghian K, Al-Sarawi S F, Abbott D 2010 Proc. R. Soc. A 466 2175
[5] Biolek Z, Biolek D, Biolkov V 2009 Radio. Eng. 18 210
[6] Pershin Y V, Di V M 2008 Phys. Rev. B 78 3309
[7] Jo S H, Kim K H, Lu W 2009 Nano Lett. 9 870
[8] Yang J, Wang L D, Duan S K 2016 Sci. China Inf. Sci. 46 391
[9] Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2015 Neurocomputing 171 23
[10] Wang L D, Duan M T, Duan S K, Hu X F 2014 Sci. China Inf. Sci. 44 920
[11] Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364
[12] Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 417
[13] Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205
[14] Zhong G Q, Man K F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 2907
[15] Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 54 2180
[16] Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[17] Min G Q, Wang L D, Duan S K 2015 Acta Phys. Sin. 64 210507 (in Chinese) [闵国旗, 王丽丹, 段书凯 2015 64 210507]
[18] Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 7
[19] Wang L D, Duan S K 2012 Abstr. Appl. Anal. 2012 2012
[20] Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 61 110502]
[21] Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[22] Wang Z L 2008 Comput. Eng. Appl. 44 84 (in Chinese) [王忠林 2008 计算机工程与应用 44 84]
[23] Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 63 060501]
[24] Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xi'an Electronic Sience and Technology University Press) pp126-148 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第126-148页]
[25] Vaněčk A, Člikovsk S 1996 Control Systems: From Linear Analysis to Synthesis of Chaos (London: Prentice Hall International Ltd.) pp10-121
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