Skip to main content
SpringerLink
Log in

A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator

  • Chapter
  • First Online:
Book cover Advances in Chaos Theory and Intelligent Control

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 337))

Abstract

In this chapter, a novel design method of a nonlinear resistor of type-N consisting of a memristor emulator circuit in parallel with a negative resistor, is presented. The proposed emulator is built with second-generation current conveyors (CCII) and passive elements and its pinched hysteresis loop is holding up to 20 kHz. As an example of using the designed nonlinear resistor, the simple non-autonomous Lacy circuit is chosen. The numerical as well as the simulation results, by using SPICE, reveal the richness of circuit’s dynamical behavior confirming the usefulness of the specific design method. The increased complexity that the nonlinear resistor with memristor gives to the circuit is a consequence of the effect of both signals frequency and amplitude to the memristors pinched hysteresis loop. Furthermore, the ease of the specific design method makes this proposal a very attractive option for the design of nonlinear resistors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adhikari SP, Yang C, Kim H, Chua LO (2012) Memristor bridge synapse-based neural network and its learning. IEEE Trans Neural Netw Learn Syst 23(9):1426–1435

    Article  Google Scholar 

  2. Arena P, Caponetto R, Fortuna L, Manganaro G (1997) Cellular neural networks to explore complexity. Soft Comput 1(3):120–136

    Article  Google Scholar 

  3. Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, vol 581. Springer, Germany

    Google Scholar 

  4. Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, vol 575. Springer, Germany

    Google Scholar 

  5. Azar AT, Vaidyanathan S (2015) Handbook of research on advanced intelligent control engineering and automation. IGI Global, USA

    Google Scholar 

  6. Banerjee S (2011) Chaos synchronization and cryptography for secure communications: applications for encryption. IGI Global, USA

    Book  Google Scholar 

  7. Banerjee S, Mitra M, Rondoni L (2011) Applications of chaos and nonlinear dynamics in engineering, vol 1. Springer, Germany

    Google Scholar 

  8. Bao BC, Xu JP, Zhou GH, Ma ZH, Zou L (2011) Chaotic memristive circuit: equivalent circuit realization and dynamical analysis. Chin Phys B 20(12):120502

    Article  Google Scholar 

  9. Bo-Cheng B, Jian-Ping X, Gua-Hua Z, Zheng-Hua M, Ling Z (2011) Chaotic memristive circuit: equivalent circuit realization and dynamical analysis. Chin Phys B 20(12):1–6

    Google Scholar 

  10. Bo-Cheng B, Fei F, Wei D, Sai-Hu P (2013) The voltage-current relationship and equivalent circuit implementation of parallel flux-controlled memristive circuits. Chin Phys B 22(6):1–6

    Google Scholar 

  11. Bonchev DD, Rouvray D (2005) Complexity in chemistry, biology, and ecology, mathematical and computational chemistry. Springer, USA

    Book  MATH  Google Scholar 

  12. Buscarino Fortuna L, Frasca M, Gambuzza LV, Sciuto G (2012) Memristive chaotic circuits based on cellular nonlinear network. Int J Bifurc Chaos 22(3):1250070

    Google Scholar 

  13. Chen Y, Jung G, Ohlberg D, Li X, Stewart D, Jeppesen J, Nielsen K, Stoddart J, Williams R (2003) Nanoscale molecular-switch crossbar circuits. Nanotechology 14(4):462–468

    Article  Google Scholar 

  14. Chua LO (1994) Chua’s circuit 10 years later. Int J Circuit Theory Appl 22(4):279–305

    Google Scholar 

  15. Chua LO (1994) Chua’s circuit: an overview ten year later. J Circuits Syst Comput 4(02):117–159

    Google Scholar 

  16. Chua LO, Yang L (1988) Cellular neural networks: application. IEEE Trans Circuits Syst I: Fundam Theory Appl 35(10):1273–1290

    Google Scholar 

  17. Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst I: Fundam Theory Appl 35(10):1257–1272

    Google Scholar 

  18. Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519

    Google Scholar 

  19. Chua LO, Hasler M, Moschytz GS, Neirynck J (1995) Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans Circuits Syst I: Fundam Theory Appl 42(10):559–577

    Article  MathSciNet  Google Scholar 

  20. Chua LO, Kang S (1976) Memristive devices and systems. Proc IEEE 64:209–223

    Article  MathSciNet  Google Scholar 

  21. Chua LO, Roska T (2002) Cellular neural networks and visual computing. Cambridge University Press, Cambridge

    Book  Google Scholar 

  22. Cruz JM, Chua LO (1986) A CMOS IC nonlinear resistor for Chua’s circuit. IEEE Trans Circuits Syst I 39(12):985–995

    Google Scholar 

  23. Driscoll T, Quinn J, Klein S, Kim HT, Kim BJ, Pershin YV, Ventra MD, Basov DN (2010) Memristive adaptive filters. Appl Phys Lett 97(9):093502

    Article  Google Scholar 

  24. Elwakil A, Fouda M, Radwan A (2013) A simple model of double-loop hysteresis behavior in memristive elements. IEEE Trans Circuits Syst II: Exp Briefs 60:487–491

    Article  Google Scholar 

  25. Eve RA, Horsfall S, Lee M (1997) Chaos, complexity, and sociology: myths, models, and theories. Sage Publications

    Google Scholar 

  26. Fortuna L, Arena P, Balya D, Zarandy A (2001) Cellular neural networks: a paradigm for nonlinear spatio-temporal processing. IEEE Circuits Syst Mag 1(4):6–21

    Article  Google Scholar 

  27. Goras L, Chua LO, Leenaerts DM (1995) Turing patterns in CNNs—part I: once over lightly. IEEE Trans Circuits Syst I: Fundam Theory Appl 42(10):602–611

    Article  Google Scholar 

  28. Hussein A, Fouda M (2013) A simple MOS realization of current controlled memristor emulator. In: Proceedings of international conference on microelectron, pp 1–4

    Google Scholar 

  29. Itoh M, Chua LO (2008) Memristor oscillators. Int J Bifurc Chaos 18(11):3183–3206

    Article  MathSciNet  MATH  Google Scholar 

  30. Itoh M, Chua LO (2011) Memristor Hamiltonian circuits. Int J Bifurc Chaos 21(09):2395–2425

    Article  MATH  Google Scholar 

  31. Itoh M, Chua LO (2013) Duality of memristor circuits. Int J Bifurc Chaos 23(1):1–50

    Article  MathSciNet  MATH  Google Scholar 

  32. Iu HH, Fitch AL (2013) Development of memristor based circuits. World Scientific Publishing, Singapore

    Book  Google Scholar 

  33. Kapitaniak T (2000) Chaos for engineers: theory, applications, and control. Springer, Germany

    Book  MATH  Google Scholar 

  34. Kennedy MP (1992) Robust op amp realization of Chuas circuit. Frequenz 46(3–4):66–80

    Google Scholar 

  35. Kennedy M, Rovatti R, Setti G (2000) Chaotic electronics in telecommunications. CRC Press

    Google Scholar 

  36. Kim H, Sah MP, Yang C, Cho S, Chua LO (2012) Memristor emulator for memristor circuit applications. IEEE Trans Circuits Syst I: Regular Papers 59(10):2422–2431

    Article  MathSciNet  Google Scholar 

  37. Kyprianidis IM, Makri AT, Stouboulos IN, Volos CK (2013) Antimonotonicity in a FitzHugh Nagumo type circuit. In: Recent advances in finite differences and applied and computational mathematics, proceedings of 2nd international conference on applied and computational mathematics (ICACM’13), pp 151–156

    Google Scholar 

  38. Kyprianidis IM, Stouboulos IN (2003) Chaotic synchronization of three coupled oscillators with ring connection. Chaos Solit Fract 17(2):939–941

    MATH  Google Scholar 

  39. Larson LL, Liu J-M, Tsimring LS (2006) Digital communications using chaos and nonlinear dynamics. Institute for Nonlinear Science

    Google Scholar 

  40. Li Y, Huang X, Guo M (2013) The generation, analysis and circuit implementation of a new memristor based chaotic system. Math Prob Eng

    Google Scholar 

  41. Matsumoto T, Chua LO, Komuro M (1985) The double scroll. IEEE Trans Circuits Syst 32(8):798–818

    Article  MathSciNet  MATH  Google Scholar 

  42. Matsumoto T, Chua LO, Tokumasu K (1986) Double scroll via a two-transistor circuit. IEEE Transa Circuits Syst I 33(8):828–835

    Article  MathSciNet  Google Scholar 

  43. Medoza-Lopez CS-LJ, Carrasco-Aguilar MA, Muniz-Montero C (2014) A floating analog memristor emulator circuit. IEEE Trans Circuits Syst II: Exp Briefs 61(5):309–313

    Article  Google Scholar 

  44. Meron E (2015) Nonlinear physics of ecosystems. CRC Press

    Google Scholar 

  45. Multu R, Karakulak E (2010) Emulator circuit of TiO\(_2\) memristor with linear dopant drift made using analog multiplier. In: National conference on electrical, electronics and computer engineering (ELECO), pp 380–384

    Google Scholar 

  46. Muthuswamy B (2010) Implementing memristor based chaotic circuits. Int J Bifurc Chaos 20(5):1335–1350

    Article  MATH  Google Scholar 

  47. Muthuswamy B, Chua LO (2010) Simplest chaotic circuit. Int J Bifurc Chaos 20(5):1567–1580

    Article  Google Scholar 

  48. Muthuswamy B, Kokate PP (2009) Memristor-based chaotic circuits. IETE Tech Rev 26(6):417–429

    Article  Google Scholar 

  49. Nakagawa M (1999) Chaos and fractals in engineering. World Scientific Publishing, Singapore

    Book  Google Scholar 

  50. Perez-Munuzuri V, Perez-Villar V, Chua LO (1993) Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths. IEEE Trans Circuits Syst I: Fundam Theory Appl 40(3):174–181

    Article  MATH  Google Scholar 

  51. Pershin YV, Ventra MD (2010) Experimental demonstration of associative memory with memristive neural networks. Neural Netw 23(7):881–886

    Google Scholar 

  52. Pershin YV, Ventra MD (2010) Practical approach to programmable analog circuits with memristors. IEEE Trans Circuits Syst I: Regular Papers 57(8):1857–1864

    Google Scholar 

  53. Pershin YV, Fontaine SL, Ventra MD (2000) Memristive model of amoeba learning. Phys Rev E 80(2):1–6

    Google Scholar 

  54. Pershin YV, Ventra MD (2008) Spin memristive systems: spin memory effects in semiconductor spintronics. Phys Rev B 78(11):1–4

    Article  Google Scholar 

  55. Pickett M, Williams R (2012) Sub-100 fJ and sub-nanosecond thermally driven threshold switching in niobium oxide crosspoint nanodevices. Nanotechnology 23(21):215202

    Article  Google Scholar 

  56. Sah MP, Yang C, Kim H, Chua LO (2012) A voltage mode memristorbridge synaptic circuit with memristor emulators. Sensors 12(3):3587–3604

    Article  Google Scholar 

  57. Sapoff M, Oppenheim R (1963) Theory and application of self-heated thermistors. Proc IEEE 51:1292–1305

    Article  Google Scholar 

  58. Shang Y, Fei W, Yu H (2012) Analysis and modeling of internal state variables for dynamic effects of nonvolatile memory devices. IEEE Trans Circuits Syst I: Regular Papers 59(9):1906–1918

    Google Scholar 

  59. Shin S, Kim K, Kang SM (2011) Memristor applications for programmable analog ICs. IEEE Trans Nanotechnol 10(2):266–274

    Article  Google Scholar 

  60. Shin S, Zheng L, Weickhardt G, Cho S, Kang S-M (2013) Compact circuit model and hardware emulation for floating memristor devices. IEEE Circuits Syst Mag 13(2):42–55

    Article  Google Scholar 

  61. Shi Z, Ran L (2004) Tunnel diode based chuas diode. In: Proceedings of IEEE 6th CAS sympoisum on emerging technologies: mobile and wireless communications, pp 217–220

    Google Scholar 

  62. Sodhi A, Gandhi G (2010) Circuit mimicking \(TiO_2\) memristor: a plug and play kit to understand the fourth passive element. Int J Bifurc Chaos 20(8):2537–2545

    Article  Google Scholar 

  63. Strogatz SH (1994) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Perseus Books, Massachutetts

    Google Scholar 

  64. Strukov D, Snider G, Stewart G, Williams R (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  65. Vaidyanathan S, Idowu B, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s Jerk systems, vol 581. Springer-Verlag GmbH, Berlin

    Google Scholar 

  66. Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system, vol 581. Springer-Verlag GmbH, Berlin

    Google Scholar 

  67. Vaidyanathan S, Azar AT (2015) Analysis, control and synchronization of a nine-term 3-D novel chaotic system, vol 581. Springer-Verlag GmbH, Berlin

    Google Scholar 

  68. Vaidyanathan S, Azar AT (2015) Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan-Madhavan chaotic systems, vol 576. Springer-Verlag GmbH, Berlin

    Google Scholar 

  69. Vaidyanathan S, Azar AT (2015) Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan-Madhavan chaotic systems, vol 576. Springer-Verlag GmbH, Berlin

    Google Scholar 

  70. Volos CK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61(12):13141322

    Google Scholar 

  71. Volos CK, Kyprianidis IM, Stouboulos IN (2013) Image encryption scheme based on continous-time chaotic systems. Nova Science Publishers

    Google Scholar 

  72. Volos CK, Kyprianidis I, Stouboulos I (2011) The memristor as an electric synapse-synchronization phenomena. In: Proceedings of international conference DSP2011, pp 1–6

    Google Scholar 

  73. Volos CK, Kyprianidis IM, Stouboulos IN (2012) Chaotic path planning generator for autonomous mobile robots. Robot Auton Syst 60(4):651656

    Article  Google Scholar 

  74. Wang X, Chen Y, Gu Y, Li H (2010) Spintronic memristor temperature sensor. IEEE Electr Device Lett 31(1):20–22

    Article  Google Scholar 

  75. Wang L, Zhang C, Chen L, Lai J, Tong J (2012) A novel memristor-based rSRAM structure for multiple-bit upsets immunity. IEICE Electr Exp 9(9):861–867

    Article  Google Scholar 

  76. Yang JJ, Strukov DB, Stewart DR (2013) Memristive devices for computing. Nat Nanotechnol 8(1):13–24

    Article  Google Scholar 

  77. Yang C, Choi H, Park S, Kim MPSH, Chua LO (2015) A memristor emulator as a replacement of a real memristor. Semicond Sci Technol 30(1):015007

    Article  Google Scholar 

  78. Yesil A, Babacan Y, Kacar F (2014) A new DDCC based memristor emulator circuit and its applications. J Microelectr 45(3):282–287

    Article  Google Scholar 

  79. Yu D, Iu HH-C, Fitch AL, Liang Y (2014) Memristor emulator for memristor circuit applications. Float Memristor Emul Based Relax Oscil 61(10):2888–2896

    Google Scholar 

  80. Zhang W-B (2005) Differential equations, bifurcations, and chaos in economics, vol 68. World Scientific Publishing, Singapore

    MATH  Google Scholar 

  81. Zhang W-B (2006) Discrete dynamical systems, bifurcations and chaos in economics, mathematics in science and engineering, vol 204. Elsevier, Netherlands

    Google Scholar 

  82. Zhong GQ (1986) Implementation of Chuas circuit with a cubic nonlinearity. IEEE Trans Circuits Syst I 41(12):939–941

    Google Scholar 

  83. Zhu Q, Azar AT (2015) Complex system modeling and control through intelligent soft computations, vol 319. Springer, Germany

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Ch.K. Volos, J. O. Maaita, A. Giakoumis, I. M. Kyprianidis & I. N. Stouboulos

  2. Research and Development Centre, Vel Tech University, Tamil Nadu, India

    S. Vaidyanathan

  3. School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam

    V.-T. Pham

Authors
  1. Ch.K. Volos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Vaidyanathan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V.-T. Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. O. Maaita
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Giakoumis
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. I. M. Kyprianidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. I. N. Stouboulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ch.K. Volos .

Editor information

Editors and Affiliations

  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Volos, C. et al. (2016). A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator. In: Azar, A., Vaidyanathan, S. (eds) Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-30340-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30340-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30338-3

  • Online ISBN: 978-3-319-30340-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation