Skip to main content
SpringerLink
Log in

Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Josephson junction resonators are the devices which exhibit complex behaviours as a consequence of their inductive properties. Even though the insulating medium between Josephson junctions (JJs) is normally considered homogeneous, the fact that lithography is used to form the layer, it has fractal substrates. Such JJs are identified as fractal Josephson junctions (FJJs). In this paper, a new chaotic oscillator based on memristor and FJJ has been investigated. Superconductor properties can dramatically change its operating points especially voltage and heat that are related to Josephson tunnelling. Some changes in the operating points can cause the Josephson tunnelling junctions to oscillate in different oscillation modes in very high frequencies. This can be achieved by considering the potential across the junction with its flux feedback. In order to model the magnetic flux effect, we use a memristor whose memductance function is considered as an exponential function. By varying the type of the bias current, we could observe the property of infinitely coexisting attractors in the memristor-fractal Josephson junction oscillator, which is considered as a rare phenomenon in physical circuits. The proposed Josephson-Memristor circuit model is developed, and its equilibrium points, bifurcation and Lyapunov exponents are computed. As an engineering application, modelling the trajectories of the moving object has been realized. First, the SURF algorithm, which is not affected by the scale and rotations of the object, is used in the images to identify an object that tracks the states of the proposed Josephson-Memristor circuit. In this way, the coordinates of the orbits on which the object moves were determined on the image. In order to reproduce the orbits of the specified object, the coordinate information of the object has been trained to the artificial neural network model and the orbits of the object have been reproduced.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Kitamura, T., Yokoyama, M.: Effect of electronic states of triphenylamine derivatives on their charge transport properties. J. Applied. Phys 30(9B), L1656 (1991)

    Article  Google Scholar 

  2. Kruchinin, S.P., Klepikov, V.F., Novikov, V.E., Kruchinin, D.S.: Nonlinear current oscillations in the fractal Josephson junction. Mater. Sci. Pol 23(4), 1009 (2005)

    Google Scholar 

  3. Uchida, A., Lida, H., Maki, N., Osawa, M., Yoshimori, S.: Chaotic oscillations in Josephson tetrode. IEEE Trans. Appl. Supercond. 14(4), 2064 (2004)

    Article  Google Scholar 

  4. Huberman, B.A., Crutchfield, J.P., Packard, N.H.: Noise phenomena in Josephson junctions. Appl. Phys. Lett. 37, 750 (1980)

    Article  Google Scholar 

  5. Rajagopal, K.J.P.S., Roy, B.K., Karthikeyan, A.: Dissipative and conservative chaotic nature of a new quasi-periodically forced oscillator with megastability. Chinese J. Phys. 58, 263–272 (2019)

    Article  Google Scholar 

  6. Uchida, A., Davis, P., Itaya, S.: Generation of information theoretic secure keys using a chaotic semiconductor laser. Appl. Phys. Lett. 83(15), 3213–3215 (2003)

    Article  Google Scholar 

  7. Sugiura, T., Yamanashi, Y., Yoshikawa, N.: Demonstration of 30 Gbit/s generation of superconductive true random number generator. IEEE Trans. Appl. Supercond. 21(3), 843 (2011)

    Article  Google Scholar 

  8. Kennedy, M.P., Rovatti, R., Setti, G., Raton, B.: Chaotic Electronics in Telecommunications. Boca Raton CRC (2000)

  9. Kautz, R.L.: Chaotic states of RF-biased Josephson junctions. J. Appl. Phys. 52(10), 6241–6246 (1981)

    Article  Google Scholar 

  10. Kornev, V.K., Semenov, V.K.: Chaotic and stochastic phenomena in superconducting quantum interferometers. IEEE Trans. Magn. 19, 633–636 (1983)

    Article  Google Scholar 

  11. Kruchinin, S., Novikov, V., Klepikov, V.: Nonlinear current oscillations in a Josephson junction with fractal radioisotop composite. Metrol. Meas. Syst XV(3), 381 (2008)

    Google Scholar 

  12. Iansiti, M., Qing, H., Westervelt, R.M., Tinkham, M.: Noise and Chaos in a Fractal Basin Boundary Regime of a Josephson Junction. Phys. Rev. Lett. 55(7), 746 (1985)

    Article  Google Scholar 

  13. Mehmet Canturk, I.N.A.: Chaotic Dynamics of a Fractal Josephson Junction. J Supercond Nov Magn (2014)

  14. Dong, X.-J., Hu, Y.-F., Wu, Y.-Y., Zhao, J., Wan, Z.-Z.: A fractal model for effective thermal conductivity of isotropic porous silica low-k materials. Chin. Phys. Lett. 27(4), 044401 (2010)

    Article  Google Scholar 

  15. Boming, Y., Li, J.: Some fractal characters of porous media. Fractals 09(03), 365–372 (2001)

    Article  Google Scholar 

  16. Dana, S.K., Sengupta, D., Edoh, K.: Chaotic dynamics in Josephson junction. IEEE Trans. Cir. Sys. I: Fund. Theo. Appl. 48(8), 950–956 (2001)

    Google Scholar 

  17. Njitacke, Z.T., Kengne, J., Kengne, L.K.: Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit. Chaos, Solitons Fractals 105, 77–91 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Maguire, L.P., Roche, B., McGinnity, T.M., McDaid, L.: Predicting a chaotic time series using a fuzzy neural network. Inf. Sci. 112(4), 125–136 (1998)

    Article  MATH  Google Scholar 

  19. Principe, J.C., Rathie, A., Kuo, J.-M.: Prediction of chaotic time series with neural networks and the issue of dynamic modeling. Int. J. Bifurcation and Chaos 2(04), 989–996 (1992)

    Article  MATH  Google Scholar 

  20. Gómez-Gil, P., et al.: A neural network scheme for long-term forecasting of chaotic time series. Neural Process. Lett. 33(3), 215–233 (2011)

    Article  Google Scholar 

  21. Guerra, F.A., Coelho, L.D.S.: Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization. Chaos, Solitons Fractals 35(5), 967–979 (2008)

    Article  MATH  Google Scholar 

  22. Guerra, F.A. Coelho, L.: Radial basis neural network learning based on particle swarm optimization to multistep prediction of chaotic Lorenz’s system. In: Fifth International Conference on Hybrid Intelligent Systems (HIS’05). IEEE (2005)

  23. Fırat, U.: Kaotik zaman serilerinin yapay sinir ağlarıyla kestirimi: Deprem verisi durumu (2006)

  24. Hanbay, D., Türkoğlu, İ., Demir, Y.: Chua Devresinin yapay sinir ağı ile modellenmesi. Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 19(1), 67–72 (2007)

    Google Scholar 

  25. Faqih, A., Kamanditya, B., Kusumoputro, B.: Multi-Step Ahead Prediction of Lorenz’s Chaotic System Using SOM ELM-RBFNN. In: 2018 International Conference on Computer, Information and Telecommunication Systems (CITS). IEEE (2018)

  26. Ashraf-Modarres, A., Johari-Majd, V.: On-line Identification and Prediction of Lorenz’s Chaotic System Using Chebyshev Neural Networks (2007)

  27. Aqil, M., et al.: Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool. J Environ. Manag. 85(1), 215–223 (2007)

    Article  Google Scholar 

  28. Shen, Z., et al.: A novel time series forecasting model with deep learning. Neurocomputing (2019)

  29. Dedeoğlu, Y., et al., Videoda Nesne Sınıflandırması için Siluet Tabanlı Yöntem. Signal Processing and Communications Applications (2006) pp. 1–4

  30. Gonzalez, R.C., Woods, R.E., Eddins, S.L.: Digital image processing using MATLAB. Pearson Education India, Chennai (2004)

    Google Scholar 

  31. Brunelli, R.: Template matching techniques in computer vision: theory and practice. John Wiley & Sons, New York (2009)

    Book  Google Scholar 

  32. Cuimei, L., et al.: Human face detection algorithm via Haar cascade classifier combined with three additional classifiers. in 2017 13th IEEE International Conference on Electronic Measurement & Instruments (ICEMI). (2017). IEEE

  33. Soo, S.: Object detection using Haar-cascade Classifier, pp. 1–12. University of Tartu, Institute of Computer Science, Tartu (2014)

    Google Scholar 

  34. Dalal, N., Triggs, B., Schmid, C.: Human detection using oriented histograms of flow and appearance. In: European conference on computer vision. Springer (2006)

  35. Lei, Z., Fang, T., Li, D.: Histogram of oriented gradient detector with color-invariant gradients in Gaussian color space. Optical Eng. 49(10), 109701 (2010)

    Article  Google Scholar 

  36. Heisele, B., et al.: Hierarchical classification and feature reduction for fast face detection with support vector machines. Pattern Recogn. 36(9), 2007–2017 (2003)

    Article  MATH  Google Scholar 

  37. Kyrkou, C., Theocharides, T.: A parallel hardware architecture for real-time object detection with support vector machines. IEEE Trans. Comput. 61(6), 831–842 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. De la Torre, F. and M.J. Black. Robust principal component analysis for computer vision. In: Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001. IEEE (2001)

  39. Bartlett, M.S., Movellan, J.R., Sejnowski, T.J.: Face recognition by independent component analysis. IEEE Trans. Neural Netw. 13(6), 1450–1464 (2002)

    Article  Google Scholar 

  40. Lifkooee, M.Z., Soysal, Ö.M., Sekeroglu, K.: Video mining for facial action unit classification using statistical spatial–temporal feature image and LoG deep convolutional neural network. Mach. Vis. Appl. 30(1), 41–57 (2019)

    Article  Google Scholar 

  41. Manickam, A., et al.: Score level based latent fingerprint enhancement and matching using SIFT feature. Multimed. Tools Appl. 78(3), 3065–3085 (2019)

    Article  Google Scholar 

  42. Daş, R., Polat, B., Tuna, G.: Derin Öğrenme ile Resim ve Videolarda Nesnelerin Tanınması ve Takibi. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 31(2): 571-581

  43. Kitamura, T., Yokoyama, M.: Hole drift mobility and chemical structure of charge-transporting hydrazone compounds. J. Appl. Phys. 69, 821–826 (1991)

    Article  Google Scholar 

  44. Kingni, S.T., Kuiate, G.F., Tamba, V.K., Monwanou, A.V., Orou, J.B.C.: Analysis of a Fractal Josephson Junction with Unharmonic Current-Phase Relation. J. Supercond. Novel Magn. 32, 2295–2301 (2019)

    Article  Google Scholar 

  45. Canturk, M., Askerzade, I.: Chaotic dynamics of externally shunted Josephson junction with unharmonic CPR. J. Supercond. Novel Magn. 26, 839–843 (2013)

    Article  Google Scholar 

  46. Barash, Y.S.: Interfacial pair breaking and planar weak links with an unharrnonic current-phase relation. JETP Lett. 100, 205–215 (2014)

    Article  Google Scholar 

  47. Finger, L.: On the dynamica of coupled Josephson junction circuits. Int. J. Bifurcat. Chaos 6(7), 1363–1374 (1996)

    Article  MATH  Google Scholar 

  48. Wei, L., Fa-Qiang, W., Xi-Kui, M.: Exponential flux-controlled memristor model and its floating emulator. Chinese Phys. B 24, 118401 (2015)

    Article  Google Scholar 

  49. Sprott, J.C., Jafari, S., Khalaf, A.J.M., Kapitaniak, T.: Megastability: coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially periodic damping. Eur. Phys. J. Special Topics 226(9), 1979–1985 (2017)

    Article  Google Scholar 

  50. Zhang, G., Ma, J., Alsaedi, A., Ahmad, B., Alzahrani, F.: Dynamical behaviour and application in Josephson Junction coupled by memristor. Appl. Math. Comput. 321, 290–299 (2018)

    MathSciNet  MATH  Google Scholar 

  51. Ashraf-Modarres, A., Johari-Majd, V.: On-line Identification and Prediction of Lorenz’s Chaotic System Using Chebyshev Neural Networks. First Joint Congress on Fuzzy and Intelligent Systems, pp. 29–31. Ferdowsi University of Mashhad, Iran (2007)

    Google Scholar 

  52. Jahanshahi, H., Rajagopal, K., Akgul, A., Sari, N.N., Namazi, H., Jafari, S.: Complete analysis and engineering applications of a megastable nonlinear oscillator. Int. J. Non-Linear Mech. 107, 126–136 (2018)

    Article  Google Scholar 

  53. Prakash, P., Rajagopal, K., Singh, J.P., Roy, B.K.: Megastability in a quasi-periodically forced system exhibiting multistability, quasi-periodic behaviour, and its analogue circuit simulation. AEU – Int. J. Elect. Commun. 92, 111–115 (2018)

    Article  Google Scholar 

  54. Prakash, P., Rajagopal, K., Singh, J.P., Roy, B.K.: Megastability, Multistability in a Periodically Forced Conservative and Dissipative System with Signum Nonlinearity. Int. J. Bifurcation Chaos 28(9), 1830030 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  55. Dawson, S.P., Grebogi, C., Yorke, J.A., Kan, I., Kocak, H.: Antimonotonicity: inevitable reversals of period-doubling cascades. Phys. Lett. A 162, 249–254 (1992)

    Article  MathSciNet  Google Scholar 

  56. Li, C., Sprott, J.C.: Coexisting Hidden Attractors in a 4-D Simplified Lorenz System. Int. J. Bifurcation Chaos 24(3), 1450034 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  57. Li, C.-L., Li, H.-M., Li, W., Tong, Y.-N., Zhang, J., Wei, D.Q., Li, F.-D.: Dynamics, implementation and stability of a chaotic system with coexistence of hyperbolic and non-hyperbolic equilibria. Int. J. Electron. Commun. (AEU) 84, 199–205 (2018)

    Article  Google Scholar 

  58. Chunbiao, L., Wang, X., Chen, G.: Diagnosing multistability by offset boosting. Nonlinear Dyn. 90, 1335–1341 (2017)

    Article  MathSciNet  Google Scholar 

  59. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16(3), 285–317 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  60. Cimen, M.E., et al.: Modelling of a Chaotic System Motion in Video with Artiıficial Neural Networks. Chaos Theory and Applications. 1(1): 38–50

  61. Cimen, M.E., et al.: Modeling of Chaotic Motion Video with Artificial Neural Networks, In: Co-chair. p. 193 (2018)

  62. Çimen, M.E., et al.: Kaotik bir hareket videosunun yapay sinir ağları ile modellenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3), 23–35 (2018)

    Article  Google Scholar 

  63. Preucil, J.S.T.K.J.F.L.: FPGA Based Speeded Up Robust Features

  64. Xu Bo, Wang Junwen, L.G.D.Y.: Image Copy-move Forgery Detection Based on SURF, In: International Conference on Multimedia Information Networking and Security (2010)

  65. Barolli†, Y.S.T.O.M.I.L.: An Object Tracking System Based on SIFT and SURF Feature Extraction Methods, In: 18th International Conference on Network-Based Information Systems (2015)

  66. Köse, Y., Döküm Sektöründe Görüntü Işleme Tenkikleri Kullanilarak Parça Kontrolü, In: Elektrik-Elektronik Mühendisliği Yüksek Lisans Programı (2019)

  67. Papaefstathiou, D.B.A.N.I.: Fast and Efficient FPGA-based Feature Detection employing the SURF algorithm, In: 18th IEEE Annual International Symposium on Field-Programmable Custom Computing Machines (2010)

  68. Karakuş, P, Karabörk H.: Surf Algoritmasi Kullanilarak Uzaktan Algilama Görüntülerinin Geometrik Kaydi

  69. Bay, H., Tuytelaars, T., Van Gool, L.: Speeded-up robust features. Comput. Vis. Image Underst. 110(3), 346–359 (2008)

    Article  Google Scholar 

  70. Chen, W., Ding, S., Chai, Z., He, D., Zhang, W., Zhang, G., Peng, Q., Luo, W.: FPGA-Based Parallel Implementation of SURF Algorithm, In: IEEE 22nd International Conference on Parallel and Distributed Systems (2016)

  71. Öztemel, E.: Yapay sinir ağlari. PapatyaYayincilik, Istanbul (2003)

    Google Scholar 

  72. Norvig;, S.R.P.: Artificial Intellegence A modern Approach (2009)

Download references

Funding

This study received no funds.

Author information

Authors and Affiliations

  1. Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Anitha Karthikeyan

  2. Faculty of Technology, Department of Electrical and Electronics Engineering, Sakarya University of Applied Sciences, Sakarya, 54050, Turkey

    Murat Erhan Cimen, Akif Akgul & Ali Fuat Boz

  3. Center for Nonlinear Systems, Chennai Institite of Technology, Chennai, India

    Karthikeyan Rajagopal

Authors
  1. Anitha Karthikeyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Murat Erhan Cimen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Akif Akgul
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Fuat Boz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karthikeyan Rajagopal.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karthikeyan, A., Cimen, M.E., Akgul, A. et al. Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect. Nonlinear Dyn 103, 1979–1998 (2021). https://doi.org/10.1007/s11071-020-06159-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06159-4

Keywords

Search

Navigation