Complexity of Spatiotemporal Synchronization Activity of GaussianMap through Random Link
DOI:
https://doi.org/10.5890/JAND.2019.12.011Abstract
In this paper, we study spatiotemporal synchronization activity (STSA) of coupled Gaussian maps in a complex network. Our complex networks are changed stochastically with time. A coupled map lattice (CML) is adopted in Gaussian map as a prototype of a spatiotemporal chaotic systems with variation of parameters. A key motivation is that to determine (i) the effects of variation of randomness, (ii) the effects of variation of coupling strength ε , (iii) the effects of variation of parameter α when β is fixed and (iv) the effects of variation of β when parameter α is fixed on the synchronization behaviour. The variation of the basin size with respect to rewiring probability for different coupling strength and basin size with respect to coupling strength ε for different randomness, different parameters α and β are also plotted.References
[1] Willeboordse, F.H. (2003), The spatial logistic map as a simple prototype for spatiotemporal chaos, Chaos: An Interdisciplinary Journal of Nonlinear Science, 13(2), 533-540.
[2] Poria, S., Khan, M.A., and Nag, M. (2013), Spatiotemporal synchronization of coupled Ricker maps over a complex network, Physica Scripta, 88(1), 015004.
[3] Sinha, S. and Gupte, N. (2001), Targetting spatiotemporal patterns in extended systems and multiple coexisting attractors, Phys. Rev. E., 64, 015203.
[4] Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems, Phys. Rev. Lett, 64, 821-825.
[5] Balasubramaniam, P. and Muthukumar, P. (2014), Synchronization of chaotic systems using feedback controller: An application to Diffie Hellman key exchange protocol and ElGamal public key cryptosystem, Journal of the Egyptian Mathematical Society, 22(3), 365-372.
[6] Huang, Y., Chen, W., Ren, S., and Zheng, Z. (2018), Analysis and pinning control for generalized synchronization of delayed coupled neural networks with different dimensional nodes, Journal of the Franklin Institute.
[7] Khan, M.A., Sahoo, B., and Mondal, A.K. (2015), Control of chaos to obtain periodic behaviour via nonlinear control, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 85(1), 143-148.
[8] Pei, L., Li, Y., and Li, X. (2018), Generalized synchronization of the coupled heterogeneous chaotic systems by the inertial manifold approach, International Journal of Novel Ideas: Mathematics, 2, 14-29.
[9] Xu, F. and Yu, P. (2010), Chaos control and chaos synchronization for multi-scroll chaotic attractors generated using hyperbolic functions, Journal of mathematical analysis and applications, 362(1), 252-274.
[10] Khan, M.A. and Poria, S. (2012), Generalized synchronization of bidirectionally coupled chaotic systems, Int. J. of Applied Mathematical Research, 1, 303-313.
[11] Tarai, A., Poria, S., and Chatterjee, P. (2009), Synchronization of bidirectionally coupled chaotic Chen’s system with delay, Chaos, Solitons and Fractals, 41(1), 190-197.
[12] Khan, M.A., Mondal, A.K., and Poria, S. (2011), Three control strategies for unified chaotic system, International Journal of Applied Mechanics and Engineering, 16(2), 597.
[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] Tarai, A. and Khan, M.A. (2013), Projective synchronization of chaotic systems via backstepping design, International Journal of Applied Mechanics and Engineering, 18(3), 965-973.
[15] Xiao, Y., Tang, S., Sun, Z., and Song, X. (2018), Positive role of multiplication noise in attaining complete synchronization on large complex networks of dynamical systems, Applied Mathematical Modelling, 54, 803- 816.
[16] Ouannas, A. and Karouma, A. (2018), Different generalized synchronization schemes between integer-order and fractional-order chaotic systems with different dimensions, Differential Equations and Dynamical Systems, 26(1-3), 125-137.
[17] Gowse, V.R., Palanivel, B., and Sivaprakasam, S. (2018), Co-existence of synchronization and antisynchronization in Generalized Lorenz System with application to secure communications, arXiv preprint arXiv:1805.01122.
[18] Yuan, M., Wang, W., Luo, X., Li, L., Kurths, J., and Wang, X. (2018), Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control, Modern Physics Letters B, 32(09), 1850116.
[19] Yang, W., Yu, W., Cao, J., Alsaadi, F.E., and Hayat, T. (2018), Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen Grossberg BAM neural networks with impulses, Neural Networks, 98, 122-153.
[20] Li, C., Wang, L., Sun, S., and Xia, C. (2018), Identification of influential spreaders based on classified neighbors in real-world complex networks, Applied Mathematics and Computation, 320, 512-523.
[21] Avena-Koenigsberger, A., Misic, B., and Sporns, O. (2018), Communication dynamics in complex brain networks, Nature Reviews Neuroscience, 19(1), 17.
[22] Zengler, K., and Zaramela, L. S. (2018). The social network of microorganisms how auxotrophies shape complex communities. Nature Reviews Microbiology, 1.
[23] Losapio, G., Pugnaire, F.I., O’Brien, M.J., and Schob, C. (2018), Plant life history stage and nurse age change the development of ecological networks in an arid ecosystem, Oikos.
[24] Donges, J.F., Heitzig, J., Barfuss, W., Kassel, J.A., Kittel, T., Kolb, J.J., ... and Zimmerer, K.B. (2018), Earth system modelling with complex dynamic human societies: the copan: CORE World-Earth modeling framework, Earth System Dynamics Discussions, 1-27.
Article Metrics
Usage tracking begins September 1, 2026.