Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization

B. A. Mezatio; M. Tingue Motchongom; R. Kengne; T. Fozin Fonzin; A. Tchagna Kouanou; R. Tchitnga; A. Fomethe

doi:doi:10.11648/j.cssp.20200901.11

| Peer-Reviewed

Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization

B. A. Mezatio, M. Tingue Motchongom, R. Kengne, T. Fozin Fonzin, A. Tchagna Kouanou, R. Tchitnga, A. Fomethe

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 9, Issue 1)

Received: 8 October 2019 Accepted: 6 November 2019 Published: 13 April 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.

Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 9, Issue 1)
DOI	10.11648/j.cssp.20200901.11
Page(s)	1-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Bursting Oscillations, High Frequency, Periodically Intermittent Discrete Observation Control, Relay Coupling System, Global Synchronization

References

[1]	Pikovsky A., Rosenblum M., Kurths J. (2002) Synchronization: a universal concept in nonlinear science.
[2]	Sharma A, Shrimali M. D., Aihara K. (2014) Effect of mixed coupling on relay-coupled R¨ossler and lorenz oscillators, Physical Review E 90 (6), 062907.
[3]	koseska A., Volkov E., and Kurths J. (2013) Oscillation quenching mechanisms: Amplitude vs. oscillation death, Physics Reports 531 (4), 173-199.
[4]	Saxena G., Prasad A., Ramaswamy R. (2012) Amplitude death: The emergence of stationarity in coupled nonlinear systems, Physics Reports 521 (5), 205C228.
[5]	Karnatak R, Punetha N, Prasad A, Ramaswamy R (2010) Nature of the phase-flip transition in the synchronized approach to amplitude death, Physical Review E 82 (4), 046219.
[6]	Kerimo˘glu D. Synchronization of pendulum like systems, Ph.D. thesis, bilkent university (2011).
[7]	Pecora L. M., Carroll T. L. (1990) Synchronization in chaotic systems, Physical review letters 64 (8), 821.
[8]	Tamba V. K., Fotsin H., Kengne J., Tagne F. K., Talla P. (2015) Coupled inductors-based chaotic colpitts oscillators: Mathematical modeling and synchronization issues, The European Physical Journal Plus 130 (7), 137.
[9]	Li S., Xu W., Li R. (2007) Synchronization of two different chaotic systems with unknown parameters, Physics Letters A 361 (1-2), 98C102.
[10]	Fotsin H., Daafouz J. (2005) Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification, Physics Letters A 339 (3-5), 304C315.
[11]	Thounaojam U. S., Shrimali M. D. (2018) Phase-flip in relay oscillators via linear augmentation, Chaos, Solitons & Fractals 107, 5C12.
[12]	Liu D., Ye D. (2018) Anti-synchronization of neural networks with mixed delays, in: International Conference on Neural Information Processing, Springer, pp. 361C370.
[13]	Naderi B., Kheiri H., Heydari A. (2018) Antisynchronization of complex chaotic T-system via optimal adaptive sliding-mode and its application in secure communication, International Journal of Industrial Mathematics 10 (2), 181C192.
[14]	Cai G., Zhang Z., Feng G., Chen Q. (2019) Delay feedback impulsive control of a time-delay nonlinear complex financial networks, Indian Journal of Physics, 1C6.
[15]	Karnatak R., Ramaswamy R., Prasad A. (2007) Amplitude death in the absence of time delays in identical coupled oscillators, Physical Review E 76 (3), 035201.
[16]	Karnatak R., Ramaswamy R., Prasad A. (2009) Synchronization regimes in conjugate coupled chaotic oscillators, Chaos: An Interdisciplinary Journal of Nonlinear Science 19 (3), 033143.
[17]	Sharma A., Shrimali M. D., Prasad A., Ramaswamy R., Feudel U. (2011) Phase-flip transition in relay-coupled nonlinear oscillators, Physical Review E 84 (1), 016226.
[18]	Banerjee R., Ghosh D., Padmanaban E., Ramaswamy R., Pecora L., Dana S. K. (2012) Enhancing synchrony in chaotic oscillators by dynamic relaying, Physical Review E 85 (2), 027201.
[19]	Guti´errez R., Sevilla-Escoboza R., Piedrahita P., Finke C., Feudel U., Buldu J. M., Huerta-Cuellar G., Jaimes- Reategui R., Moreno Y., Boccaletti S. (2013) Generalized synchronization in relay systems with instantaneous coupling, Physical Review E 88 (5), 052908.
[20]	Zhao N., Sun Z., Xu W. (2018) Amplitude death induced by mixed attractive and repulsive coupling in the relay system, The European Physical Journal B 91 (1), 20.
[21]	Louodop P., Ngouonkadi E. B. M., Muruganandam P., Cerdeira H. A. (2018) Synchronization dynamics of modified relay-coupled chaotic systems, Journal of Applied Nonlinear Dynamics 7 (1), 11C24.
[22]	Kengne R., R. Tchitnga, S. Mabekou, B. R. W. Tekam, G. B. Soh, A. Fomethe, On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations, Chaos, Solitons & Fractals 111 (2018), 6C17.
[23]	Sharma A. (2019) Time delay induced partial death patterns with conjugate coupling in relay oscillators, Physics Letters A 383 (16), 1865C1870. Science Journal of Circuits, Systems and Signal Processing 2020; x(x): xx-xx 15
[24]	Zhang L., Yang Y. (2017) Lag synchronization for fractional-order memristive neural networks via period intermittent control, Nonlinear Dynamics 89 (1), 367C381.
[25]	Xu Y., Li Q., Li W. (2019) Periodically intermittent discrete observation control for synchronization of fractional-order coupled systems, Communications in Nonlinear Science and Numerical Simulation 74, 219C235.
[26]	Fan Y., Huang X., Wang Z., Xia J., Li Y. (2018) Global mittag-leffler synchronization of delayed fractionalorder memristive neural networks, Advances in Difference Equations 2018 (1), 338.
[27]	Matouk A. (2011) Chaos, feedback control and synchronization of a fractional-order modified autonomous van der polCduffing circuit, Communications in Nonlinear Science and Numerical Simulation 16 (2), 975C986.
[28]	Wan P., Jian J, Mei J. (2018) Periodically intermittent control strategies for _-exponential stabilization of fractional-order complex-valued delayed neural networks, Nonlinear Dynamics 92 (2), 247C265.
[29]	Li H. L., Hu C., Jiang H., Teng Z., Jiang Y. L. (2017) Synchronization of fractional-order complex dynamical networks via periodically intermittent pinning control, Chaos, Solitons & Fractals 103, 357C363.
[30]	Nguimdo R. M., Tchitnga R., Woafo P. (2013) Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation, Chaos: An Interdisciplinary Journal of Nonlinear Science 23 (4), 043122.
[31]	Tekam R. B. W., Kengne J., Kenmoe G. D. (2019) High frequency Colpitts’ oscillator: A simple configuration for chaos generation, Chaos, Solitons & Fractals 126, 351C360.
[32]	Tchitnga R., Mezatio B., Fozin T. F., Kengne R., Fotso P. L., Fomethe A. (2019) A novel hyperchaotic three-component oscillator operating at high frequency, Chaos, Solitons & Fractals 118, 166C180. https://doi.org/10.1016/j.chaos.2018.11.015
[33]	Kengne R., Tchitnga R, Mezatio A., Fomethe A, Litak G. (2017) Finite-time synchronization of fractionalorder simplest two-component chaotic oscillators, The European Physical Journal B 90 (5), 88.
[34]	Louodop P., Fotsin H., Kountchou M., Bowong S. (2013) Finite-time synchronization of lorenz chaotic systems: theory and circuits, Physica Scripta 88 (4), 045002.
[35]	Louodop P., Kountchou M., Fotsin H., Bowong S. (2014) Practical finite-time synchronization of jerk systems: theory and experiment, Nonlinear Dynamics 78 (1), 597C607.
[36]	Kengne R., Tchitnga R., Fomethe A., Hammouch Z. (2017) Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface, Commun Numer Anal, 233C248.
[37]	Kengne R., Tchitnga R., Kouanou A. T., Fomethe A. (2013) Dynamical properties and chaos synchronization in a fractional-order two-stage colpitts oscillator, Journal of Engineering Science & Technology Review 6 (4).
[38]	Wu R., Lu Y., Chen L. (2015) Finite-time stability of fractional delayed neural networks, Neurocomputing 149, 700C707.
[39]	Kuczma M. (2009) An introduction to the theory of functional equations and inequalities: Cauchy’s equation and Jensens inequality, Springer Science & Business Media.
[40]	Mezatio B. A., Motchongom M. T., Tekam B. R. W., Kengne R., Tchitnga R., Fomethe A. (2019) A novel memristive 6d hyperchaotic autonomous system with hidden extreme multistability, Chaos, Solitons & Fractals 120, 100C115. https://doi.org/10.1016/j.chaos.2019.01.015
[41]	Mezatio B. A., Tingue M. M., Kengne R., Kouanou A. T., Fonzin T. F., Tchitnga R. (2019) Complex dynamics from a novel memristive 6d hyperchaotic autonomous system, International Journal of Dynamics and Control, 1C21. https://doi.org/10.1007/s40435-019-00531-y
[42]	Usama M., Zakaria N. (2017) Chaos-based simultaneous compression and encryption for hadoop, PloS one 12 (1), e0168207.
[43]	Kouanou A. T., Tchiotsop D., Kengne R., Zephirin D. T., Armele N. M. A., Tchinda R. (2018) An optimal big data workflow for biomedical image analysis, Informatics in Medicine Unlocked 11, 68C74.
[44]	Kouanou A. T., Tchiotsop D., Tchinda R., Tchapga C. T., Telem A. N. K., Kengne R. (2018) A machine learning algorithm for biomedical images compression using orthogonal transforms, International Journal of Image, Graphics & Signal Processing 10 (11).
[45]	Kouanou A. T., Tchiotsop D., Fozin T. F., Mounmo B., Tchinda R. (2019) Real-time image compression system using an embedded board, Science Journal of Circuits, Systems and Signal Processing 7 (4), 81. DOI: 10.11648/j.cssp.20180704.11.

Cite This Article

Plain Text BibTeX RIS

APA Style

B. A. Mezatio, M. Tingue Motchongom, R. Kengne, T. Fozin Fonzin, A. Tchagna Kouanou, et al. (2020). Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Science Journal of Circuits, Systems and Signal Processing, 9(1), 1-15. https://doi.org/10.11648/j.cssp.20200901.11

Copy | Download

ACS Style

B. A. Mezatio; M. Tingue Motchongom; R. Kengne; T. Fozin Fonzin; A. Tchagna Kouanou, et al. Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Sci. J. Circuits Syst. Signal Process. 2020, 9(1), 1-15. doi: 10.11648/j.cssp.20200901.11

Copy | Download

AMA Style

B. A. Mezatio, M. Tingue Motchongom, R. Kengne, T. Fozin Fonzin, A. Tchagna Kouanou, et al. Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Sci J Circuits Syst Signal Process. 2020;9(1):1-15. doi: 10.11648/j.cssp.20200901.11

Copy | Download

@article{10.11648/j.cssp.20200901.11,
  author = {B. A. Mezatio and M. Tingue Motchongom and R. Kengne and T. Fozin Fonzin and A. Tchagna Kouanou and R. Tchitnga and A. Fomethe},
  title = {Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {9},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.cssp.20200901.11},
  url = {https://doi.org/10.11648/j.cssp.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20200901.11},
  abstract = {This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.},
 year = {2020}
}

Copy | Download

TY - JOUR
T1 - Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization
AU - B. A. Mezatio
AU - M. Tingue Motchongom
AU - R. Kengne
AU - T. Fozin Fonzin
AU - A. Tchagna Kouanou
AU - R. Tchitnga
AU - A. Fomethe
Y1 - 2020/04/13
PY - 2020
N1 - https://doi.org/10.11648/j.cssp.20200901.11
DO - 10.11648/j.cssp.20200901.11
T2 - Science Journal of Circuits, Systems and Signal Processing
JF - Science Journal of Circuits, Systems and Signal Processing
JO - Science Journal of Circuits, Systems and Signal Processing
SP - 1
EP - 15
PB - Science Publishing Group
SN - 2326-9073
UR - https://doi.org/10.11648/j.cssp.20200901.11
AB - This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.
VL - 9
IS - 1
ER -

Copy | Download

Author Information

B. A. Mezatio

Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
M. Tingue Motchongom

Higher Technical Teachers Training College, University of Bamenda, Bambili, Cameroon
R. Kengne

Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
T. Fozin Fonzin

Laboratory of Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
A. Tchagna Kouanou

Laboratory of Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
R. Tchitnga

Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
A. Fomethe

Unite de Recherche de Mecanique et de Modelisation des Systemes Physique (UR2MSP), Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

B. A. Mezatio, M. Tingue Motchongom, R. Kengne, T. Fozin Fonzin, A. Tchagna Kouanou, et al. (2020). Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Science Journal of Circuits, Systems and Signal Processing, 9(1), 1-15. https://doi.org/10.11648/j.cssp.20200901.11

Copy | Download

ACS Style

B. A. Mezatio; M. Tingue Motchongom; R. Kengne; T. Fozin Fonzin; A. Tchagna Kouanou, et al. Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Sci. J. Circuits Syst. Signal Process. 2020, 9(1), 1-15. doi: 10.11648/j.cssp.20200901.11

Copy | Download

AMA Style

B. A. Mezatio, M. Tingue Motchongom, R. Kengne, T. Fozin Fonzin, A. Tchagna Kouanou, et al. Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization. Sci J Circuits Syst Signal Process. 2020;9(1):1-15. doi: 10.11648/j.cssp.20200901.11

Copy | Download

@article{10.11648/j.cssp.20200901.11,
  author = {B. A. Mezatio and M. Tingue Motchongom and R. Kengne and T. Fozin Fonzin and A. Tchagna Kouanou and R. Tchitnga and A. Fomethe},
  title = {Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {9},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.cssp.20200901.11},
  url = {https://doi.org/10.11648/j.cssp.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20200901.11},
  abstract = {This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.},
 year = {2020}
}

Copy | Download