Spatiotemporal Synchronization Behaviour of Logistic Map under Nearest Wave Difference using Complex Network
DOI:
https://doi.org/10.5890/JAND.2026.03.003Abstract
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.References
[1] Zhang, B. and Liu, L. (2023), Chaos-based image encryption: review, application, and challenges, Mathematics, 11(11), 2585.
[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] Mahmoodi, K., West, B.J., and Grigolini, P. (2020), Complex periodicity and synchronization, Frontiers in Physiology, 11, 563068.
[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] 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] 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] 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] 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] Mahmoud, G.M. and Mahmoud, E.E. (2010), Complete synchronization of chaotic complex nonlinear systems with uncertain parameters, Nonlinear Dynamics, 62, 875-882.
[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] 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] 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] 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] Khan, M.A. and Poria, S. (2013), Projective synchronization of chaotic systems with bidirectional nonlinear coupling, Pramana, 81, 395-406.
[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] Khan, M.A. and Sahoo, B. (2016), Temporospatial synchronization of discrete logistic map through complex network, Optik, 127(3), 1526-1531.
[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] 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] 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] 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] 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] Sinha, S. (2024), Emergent order in adaptively rewired networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(7), 073103.
[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] 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] 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] 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] Nag, M. (2017), Bistable synchronization of coupled random network of cubic maps, Indian Journal of Physics, 91, 1589-1597.
[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] 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] 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] 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] 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] 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] 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] Weiss, E., Kann, M., and Wang, Q. (2023), Neuromodulation of neural oscillations in health and disease, Biology, 12(3), 371.
[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] Motter, A.E. and Timme, M. (2018), Antagonistic phenomena in network dynamics, Annual Review of Condensed Matter Physics, 9(1), 463-484.
Article Metrics
Usage tracking begins September 1, 2026.