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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Spatiotemporal Synchronization Behaviour of Logistic Map under Nearest Wave Difference using Complex Network

Journal of Applied Nonlinear Dynamics 15(1) (2026) 45--56 | DOI:10.5890/JAND.2026.03.003

Debjani Maity$^1$, Mohammad Ali Khan$^2$

$^1$ Department of Mathematics, Bankura University, Bankura, West Bengal, India

$^2$ Department of Mathematics, Ramananda College, Bishnupur, Bankura, West Bengal, India

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Abstract

In this study, we examine the spatiotemporal synchronization behaviour of chaotic systems within the framework of a complex network. The network is characterized by dynamic coupling connections that change stochastically over time. Specifically, we consider a one-dimensional ring of coupled chaotic logistic maps, whose evolution is governed by the nearest-neighbour wave equation. Our investigation focuses on the effects of three key parameters: the degree of randomness $(p)$, the coupling strength $(\epsilon)$, and the system parameter $(r)$. Through both analytical and numerical approaches, we conduct a linear stability analysis of the synchronized steady states. Our analytical results are found to be in excellent agreement with the numerical simulations, providing a comprehensive understanding of the synchronization dynamics in this complex system.

Acknowledgments

This research is supported by Department of Science and Technology and Biotechnology, West Bengal scheme vide memo no 232 (sanc)/ST/P/S and T/16G-32/2018, Dated 20.02.2019.

References

  1. [1] Zhang, B. and Liu, L. (2023), Chaos-based image encryption: review, application, and challenges, Mathematics, 11(11), 2585.
  2. [2] Abd Latiff, F.N. and Mior Othman, W.A. (2022), Implementation of synchronization of multi-fractional-order of chaotic neural networks with a variety of multi-time-delays: studying the effect of double encryption for text encryption, Plos One, 17(7), e0270402.
  3. [3] Mahmoodi, K., West, B.J., and Grigolini, P. (2020), Complex periodicity and synchronization, Frontiers in Physiology, 11, 563068.
  4. [4] Liao, T.L., Wan, P.Y., and Yan, J.J. (2022), Design and synchronization of chaos-based true random number generators and its FPGA implementation, IEEE Access, 10, 8279-8286.
  5. [5] Liao, T.L., Chen, H.C., Peng, C.Y., and Hou, Y.Y. (2021), Chaos-based secure communications in biomedical information application, Electronics, 10(3), 359.
  6. [6] Vaseghi, B., Pourmina, M.A., and Mobayen, S. (2017), Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding-mode control, Nonlinear Dynamics, 89, 1689-1704.
  7. [7] Boaretto, B.R.R., Budzinski, R.C., Prado, T.L., Kurths, J., and Lopes, S.R. (2018), Neuron dynamics variability and anomalous phase synchronization of neural networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(10), 103106.
  8. [8] Wright, J.J. and Liley, D.T.J. (1996), Dynamics of the brain at global and microscopic scales: neural networks and the EEG, Behavioral and Brain Sciences, 19(2), 285-295.
  9. [9] Mahmoud, G.M. and Mahmoud, E.E. (2010), Complete synchronization of chaotic complex nonlinear systems with uncertain parameters, Nonlinear Dynamics, 62, 875-882.
  10. [10] Liu, J., Chen, G., and Zhao, X. (2021), Generalized synchronization and parameters identification of different-dimensional chaotic systems in the complex field, Fractals, 29(4), 2150081.
  11. [11] Mahmoud, G.M. and Mahmoud, E.E. (2010), Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems, Nonlinear Dynamics, 61, 141-152.
  12. [12] Banerjee, T., Biswas, D., and Sarkar, B.C. (2013), Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system, Nonlinear Dynamics, 72, 321-332.
  13. [13] Khan, M.A., Pal, S.N., and Poria, S. (2012), Generalized anti-synchronization of different chaotic systems, International Journal of Applied Mechanics and Engineering, 17(1), 83.
  14. [14] Khan, M.A. and Poria, S. (2013), Projective synchronization of chaotic systems with bidirectional nonlinear coupling, Pramana, 81, 395-406.
  15. [15] Poria, S., Khan, M.A., and Nag, M. (2013), Spatiotemporal synchronization of coupled Ricker maps over a complex network, Physica Scripta, 88(1), 015004.
  16. [16] Khan, M.A. and Sahoo, B. (2016), Temporospatial synchronization of discrete logistic map through complex network, Optik, 127(3), 1526-1531.
  17. [17] Khan, M.A., Maity, D., and Jabeen, S.D. (2019), Spatiotemporal synchronization in asymmetrically bidirectionally coupled neurons over a complex network, International Journal of Modern Physics B, 33(19), 1950213.
  18. [18] Khan, M.A., Maity, D., and Jabeen, S.D. (2022), Spatiotemporal synchronization of diffusively coupled modified logistic map under complex network, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 92(2), 147-156.
  19. [19]  Wang, J.L., Chen, G.Z., Qin, T.F., Ni, W.S., and Wang, X.M., (1998), Synchronizing spatiotemporal chaos in coupled map lattices via active-passive decomposition, Physical Review E, 58(3), 3017.
  20. [20] Marwan, N. and Kurths, J. (2015), Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(9), 097609.
  21. [21] Szmoski, R.M., Pereira, R.F., and de Souza Pinto, S.E. (2013), Effective dynamics for chaos synchronization in networks with time-varying topology, Communications in Nonlinear Science and Numerical Simulation, 18(6), 1491-1498.
  22. [22] Sinha, S. (2024), Emergent order in adaptively rewired networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(7), 073103.
  23. [23] Li, H. and Min, F. (2024), Large-scale memristive Rulkov ring-star neural network with complex spatio-temporal dynamics, IEEE Transactions on Industrial Informatics, in press.
  24. [24] Nag, M. and Poria, S. (2016), Synchronization in a network of delay-coupled maps with stochastically switching topologies, Chaos, Solitons and Fractals, 91, 9-16.
  25. [25] Nag, M. and Poria, S. (2020), Effects of time delay on the synchronized states of globally coupled network, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(9), 093110.
  26. [26] Nag, M. and Poria, S. (2015), Synchronized states and multistability in a random network of coupled discontinuous maps, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(8), 083119.
  27. [27] Nag, M. (2017), Bistable synchronization of coupled random network of cubic maps, Indian Journal of Physics, 91, 1589-1597.
  28. [28] Kumar, A., Agrawal, V., and Sinha, S. (2015), Spatiotemporal regularity in networks with stochastically varying links, European Physical Journal B, 88, 1-8.
  29. [29] Jampa, M.P.K., Sonawane, A.R., Gade, P.M., and Sinha, S. (2007), Synchronization in a network of model neurons, Physical Review E, 75(2), 026215.
  30. [30] Poria, S., Shrimali, M.D., and Sinha, S. (2008), Enhancement of spatiotemporal regularity in an optimal window of random coupling, Physical Review E, 78(3), 035201.
  31. [31] Yang, C., Zhang, H., Li, X., He, Z., and Li, J. (2023), Analysis of spatial and temporal characteristics of major natural disasters in China from 2008 to 2021 based on mining news database, Natural Hazards, 118(3), 1881-1916.
  32. [32] Li, F., Yan, H., Jin, G., Liu, Y., Li, Y., and Jin, D. (2022), Automated spatio-temporal synchronous modeling with multiple graphs for traffic prediction, in Proceedings of the 31st ACM International Conference on Information and Knowledge Management, 1084-1093.
  33. [33] Lai, Z. and Ling, Q. (2023), A dual spatio-temporal network for short-term wind power forecasting, Sustainable Energy Technologies and Assessments, 60, 103486.
  34. [34] Ramírez-Ávila, G.M., Kurths, J., Depickere, S., and Deneubourg, J.L. (2019), Modeling fireflies synchronization: a mathematical modeling approach from nonlinear dynamics to complex systems, 131-156.
  35. [35] Weiss, E., Kann, M., and Wang, Q. (2023), Neuromodulation of neural oscillations in health and disease, Biology, 12(3), 371.
  36. [36] Ubeysinghe, S., Kankanamge, D., Thotamune, W., Wijayaratna, D., Mohan, T.M., and Karunarathne, A. (2023), Spatiotemporal optical control of Gaq-PLCB interactions, ACS Synthetic Biology, 13(1), 242-258.
  37. [37] Motter, A.E. and Timme, M. (2018), Antagonistic phenomena in network dynamics, Annual Review of Condensed Matter Physics, 9(1), 463-484.

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