Difference Synchronization of Fractional Order Chaotic Systems Via Active Control


  • Abidemi Emmanuel Adeniji Bells University of Technology Ota, Ogun State
  • Ayotunde Abel Ajayi Federal College of Education (Technical) Akoka, Yaba Lagos, Nigeria.
  • Abiodun Isiaka Egunjobi Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
  • Kayode Stephen Ojo University of Lagos, Akoka, Yaba Lagos, Nigeria.


Memristors and meminductors, fractional-order chaotic systems, difference synchronization, active control, numerical simulations


Communication in Physical Sciences, 2024, 11(3): 373-381

Authors: Abidemi Emmanuel Adeniji., Ayotunde Abel Ajayi, Abiodun Isiaka Egunjobi. and Kayode Stephen Ojo

Received: 12 Janary 2024/Accepted: 07 May2024

The integration of memristors and meminductors into fractional-order chaotic systems has opened up new avenues for exploring complex dynamics. This research investigates difference synchronization in memristive and meminductive fractional-order chaotic systems evolving from diverse initial conditions. Active control techniques are employed to achieve difference synchronization among three such systems. Numerical simulations validate the effectiveness of the active control techniques. This study contributes to the understanding of synchronization in complex systems and offers insights into potential applications.


Download data is not yet available.

Author Biographies

Abidemi Emmanuel Adeniji, Bells University of Technology Ota, Ogun State

Department of Physical Sciences

Ayotunde Abel Ajayi, Federal College of Education (Technical) Akoka, Yaba Lagos, Nigeria.

Department of Physics

Abiodun Isiaka Egunjobi, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

Department of Physics

Kayode Stephen Ojo, University of Lagos, Akoka, Yaba Lagos, Nigeria.

Department of Physics


Al Themairi, A., Tarek, M., El Hameed, A., & Farghaly, A. A. (2022). Tracking Control Method for Double Compound–Combination Synchronization of Fractional Chaotic System and its Application in Secure Communication (ID 5301689). https://doi.org/10.1155/2022/5301689

Borah, M., & Roy, B. K. (2017). Switching Synchronization Control Between Integer-Order and Fractional-Order Dynamics of a Chaotic System. In IEEE Indian Control Conference (pp. 456–461). IIT Guwahati, India.

Borah, M., & Roy, B. K. (2020). Systematic Construction of High Dimensional Fractional-Order Hyperchaotic Systems. Chaos, Solitons and Fractals, 131, 109539. https://doi.org/10.1016/j.chaos.2020.109539

Borah, M., & Roy, B. K. (2021). Hidden Multistability in Four Fractional-Order Memristive Meminductive and Memcapacitive Chaotic Systems With Bursting and Boosting Phenomena. European Physical Journal Special Topics, 230, 1773–1783.

Boulaaras, S., Jan, R., & Pham, V. T. (2023). Recent Advancement of Fractional Calculus and its Application in Physical Systems. Eur. Phys. J. Spec. Top., 232, 2347-2350. https://doi.org/10.1140/epjs/s11734-023-01002-4

Dongmo, E. D., Ojo, K. S., Woafo, P., & Njah, A. N. (2018). Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design. Journal of Computational and Nonlinear Dynamics, 13(5). https://doi.org/10.1115/1.4039626

Hegazi, A. S., Ahmed, E., & Matouk, A. E. (2013). On Chaos Control and Synchronization of the Commensurate Fractional Order Liu System. Commun. Nonlinear Sci. Numer. Simul., 18(5), 1193–1202.

Li, G. H., Zhou, S. P., & Yang, K. (2006). Generalized Projective Synchronization Between Two Different Chaotic Systems Using Active Back Stepping Control. Phys. Lett. A, 355(4–5), 326–330.

Magin, R. L. (2010). Fractional Calculus Models of Complex Dynamics in Biological Tissues. Computers and Mathematics with Applications, 59, 1586-1593.

Mitkowski, W., Dlugosz, M., & Skruch, P. (2022). Selected Engineering Applications of Fractional-Order Calculus. In P. Kulczycki, J. Korbicz, & J. Kacprzyk (Eds.), Fractional Dynamical Systems: Methods, Algorithms and Applications (pp. 402). Springer. https://doi.org/10.1007/978-3-030-89972-1_12

Ogunjo, S., Ojo, K. S., & Fuwape, I. A. (2017). Comparison of Three Different Synchronization Schemes for Fractional Chaotic Systems. Studies in Computational Intelligence, 688, 471-495. https://doi.org/10.1007/978-3-030-89972-1_12

Ojo, K. S., Njah, A. N., & Olusola, O. I. (2015). Compound-Combination Synchronization of Chaos in Identical and Different Orders Chaotic Systems. Arch. Control Sci., 25(4), 463–49.

Ojo, K. S., Njah, A. N., & Olusola, O. I. (2016). Generalized Combination-Combination Synchronization of Chaos in Identical Orders Chaotic Systems. J. Appl. Nonlinear Dyn., 5(1), 43–58.

Ojo, K. S., Samuel T. Ogunjo, S. T., & Fuwape, I. A. (2022). Modified Hybrid Combination Synchronization of Chaotic Fractional Order Systems. Application of Soft Computing, 26, 11865 – 11872.

Pecora, L. M., & Carroll, T. L. (1990). Synchronization in Chaotic Systems. Physical Review Letters, 64, 821–825.

Podlubny, I. (1999). Fractional Differential Equations. Academic Press.

Razminia, A., & Baleanu, D. (2013). Complete Synchronization of Commensurate Fractional Order Chaotic Systems Using Sliding Mode Control. Mechatronics, 23, 873–879.

Serdouk, F., Boumali, A., & Sibatov, R. T. (2023). Fractional Model of Multiple Trapping with Charge Leakage: Transient Photoconductivity and Transit-Time Dispersion. Fractal Fract., 7(3), 243. https://doi.org/10.3390/fractalfract7030243

Song, S., Song, X., Pathak, N., & Tejado, I. (2017). Multi-switching Adaptive Synchronization of Two Fractional-Order Chaotic Systems with Different Structure and Different Order. International Journal of Control, Automation and Systems, 15, 1524-1535. https://doi.org/10.1007/s12555-016-0097-4

Sourav, K., Pal, B. K., Roy, P. K., & Dana, S. K. (2012). Lag Synchronization and Scaling of Chaotic Attractor in Coupled System.

Taghvafard, H., & Erjaee, G. H. (2011). Phase and Anti-Phase Synchronization of Fractional Order Chaotic Systems Via Active Control. Commun. Nonlinear Sci. Numer. Simul., 16(10), 4079–4088.

Tang, T. Q., Shah, E., Bonyah, E., Jan, R., Shutaywi, M., & Alreshidi, N. (2022). Modelling and Analysis of Breast Cancer With Adverse Reactions of Chemotherapy Treatment Through Fractional Derivative. Comput. Math. Methods Med.,pp. 1-9.

Valentim, A., Rabi, J. A., David, S. A., & Tenreiro Machado, J. A. (2021). On Multistep Tumor Growth Models of Fractional Variable-Order. Biosystems, 199, 104294.

Wang, C. (2018). Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems. Advances in Mathematical Physics, 1, https://doi.org/10.1155/2018/3545083

Wang, H., Liang, H., Zan, P. & Miao, Z., (2016); A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation; Journal of Control Science and Engineering, 2016(1) ID5975491, https://doi.org/10.1155/2016/5975491.

Xinyu, G., Jiawu, Y., Santo, B., Huizhen, Y. & Jun, M., (2021); A New Image Encryption Scheme Based on Fractional Order Hyperchaotic System and Multiple Image Fusion; Sci. Rep., 11, 15737. https://doi.org/10.1038/s41598-021-94748-7.

Yang, C., Cai, H. & Zhou, P., (2016); Compound; generalized Function Projective Synchronization for Fractional-Order Chaotic Systems. Disc. Dyn. Nature Soc.

Yang, Q., Chen, D., Zhao, T., et al, (2016); Fractional Calculus in Image Processing: A Review, FCAA 19, 1222 – 1249, https://doi.org/10.1515/fca-2016-0063.

Yu, H., Wang, J., Deng, B., Wei, X., Wong, Y. K., Chan, W. L., Tsang, K. M. & Yu, Z., (2011); Chaotic Phase Synchronization in Small-World Networks of Bursting Neurons, Chaos: An Interdisciplinary Journal of Nonlinear Science; https://doi.org/10.1063/1.3565027.

Zhang, X. & Wu, R., (2020); Modified Prrojective Synchronization of Fractional-Order Chaotic Systems with Different Dimensions; Acta Mathematicae Applicatae Sinica, 36, 527-538.

Zhou, P. & Zhu, P., (2017); A Practical Synchronization Approach for Fractional- Order Chaotic Systems, Nonlinear Dynamics, 89, 1719-1726.