Emergent Behaviors in Coupled Multi-scroll Oscillators in Network with Subnetworks

Yıl 2024, Cilt: 6 Sayı: 2, 122 - 130

Adrıana Ruiz-silva Bahia Betzavet Cassal-quiroga Eber J. ávila-martínez Hector Gilardi-velázquez

https://doi.org/10.51537/chaos.1376501

Öz

This paper presents the emergence of two collective behaviors in interconnected networks. Specifically, the nodes in these networks belong to a particular class of piece-wise linear systems. The global topology of the network is designed in the form of connected subnetworks, which do not necessarily share the same structure and coupling strength. In particular, it is considered that there are two levels of connection, the internal level is related to the connection between the nodes of each subnetwork; while the external level is related to connections between subnetworks. In this configuration, the internal level is considered to provide lower bounds on the coupling strength to ensure internal synchronization of subnetworks. The external level has a relevant value in the type of collective behavior that can be achieved, for which, we determine conditions in the coupling scheme, to achieve partial or complete cluster synchronization, preserving the internal synchronization of each cluster. The analysis of the emergence of stable collective behavior is presented by using Lyapunov functions of the different coupling. The theoretical results are validated by numerical simulations.

Anahtar Kelimeler

Network of subnetworks, Multi-scroll systems, Synchronization, PWL systems

Kaynakça

• Arellano-Delgado, A., R. M. López-Gutiérrez, M. Á. Murillo- Escobar, and C. Posadas-Castillo, 2023 Master–slave outer synchronization in different inner–outer coupling network topologies. Entropy 25: 707.
• Arenas, A., A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, 2008 Synchronization in complex networks. Physics reports 469: 93–153.
• Ávila-Martínez, E. J., J. L. Echenausía-Monroy, and A. Ruíz-Sílva, 2022 Multi-scroll systems synchronization on strongly connected digraphs. Chaos Theory and Applications 4: 205–211.
• Boccaletti, S., G. Bianconi, R. Criado, C. I. Del Genio, J. Gómez- Gardenes, et al., 2014 The structure and dynamics of multilayer networks. Physics reports 544: 1–122.
• Boccaletti, S., P. De Lellis, C. del Genio, K. Alfaro-Bittner, R. Criado, et al., 2023 The structure and dynamics of networks with higher order interactions. Physics Reports 1018: 1–64.
• Campos-Cantón, E., 2016 Chaotic attractors based on unstable dissipative systems via third-order differential equation. International Journal of Modern Physics C 27: 1650008.
• Campos-Cantón, E., J. G. Barajas-Ramirez, G. Solis-Perales, and R. Femat, 2010 Multiscroll attractors by switching systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 20.
• Campos-Cantón, E., R. Femat, and G. Chen, 2012 Attractors generated from switching unstable dissipative systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 22.
• Chen, G., X. Wang, and X. Li, 2014 Fundamentals of complex networks : models, structures, and dynamics .
• Cozzo, E., G. F. de Arruda, F. A. Rodrigues, and Y. Moreno, 2016 Multilayer networks: metrics and spectral properties. Interconnected networks pp. 17–35.
• De Domenico, M., A. Solé-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, et al., 2013 Mathematical formulation of multilayer networks. Physical Review X 3: 041022.
• Echenausía-Monroy, J. and G. Huerta-Cuéllar, 2020 A novel approach to generate attractors with a high number of scrolls. Nonlinear Analysis: Hybrid Systems 35: 100822.
• Gilardi-Velázquez, H. E., L. Ontañón-García, D. G. Hurtado- Rodriguez, and E. Campos-Cantón, 2017 Multistability in piecewise linear systems versus eigenspectra variation and round function. International Journal of Bifurcation and Chaos 27: 1730031.
• Huang, L., Y.-C. Lai, and R. A. Gatenby, 2008 Alternating synchronizability of complex clustered networks with regular local structure. Physical Review E 77: 016103.
• Katakamsetty, V. R., D. Rajani, and P. Srikanth, 2023 A study on community detection in multilayer networks. Journal of High Speed Networks pp. 1–13.
• Kenett, D. Y., M. Perc, and S. Boccaletti, 2015 Networks of networks– an introduction. Chaos, Solitons & Fractals 80: 1–6.
• Liu, S., B. Xu, Q. Wang, and X. Tan, 2023 Synchronizability of multilayer star-ring networks with variable coupling strength. Electronic Research Archive 31: 6236–6259.
• Lu, R., W. Yu, J. Lü, and A. Xue, 2014 Synchronization on complex networks of networks. IEEE transactions on neural networks and learning systems 25: 2110–2118.
• Méndez-Ramírez, R., A. Arellano-Delgado, and M. Á. Murillo- Escobar, 2023 Network synchronization of macm circuits and its application to secure communications. Entropy 25: 688.
• Mucha, P. J., T. Richardson, K. Macon, M. A. Porter, and J.-P. Onnela, 2010 Community structure in time-dependent, multiscale, and multiplex networks. science 328: 876–878.
• Pecora, L. M. and T. L. Carroll, 1998 Master stability functions for synchronized coupled systems. Physical review letters 80: 2109. Ruiz-Silva, A., 2021 Synchronization patterns on networks of pancreatic β-cell models. Physica D: Nonlinear Phenomena 416: 132783.
• Ruiz-Silva, A. and J. G. Barajas-Ramírez, 2018 Cluster synchronization in networks of structured communities. Chaos, Solitons & Fractals 113: 169–177.
• Ruiz-Silva, A., B. Cassal-Quiroga, and H. Gilardi-Velázquez, 2022a Anti-synchronization in a pair of coupled multistable systems. In Complex Systems and Their Applications: Second International Conference (EDIESCA 2021), pp. 23–37, Springer.
• Ruiz-Silva, A., B. Cassal-Quiroga, G. Huerta-Cuellar, and H. Gilardi-Velázquez, 2022b On the behavior of bidirectionally coupled multistable systems. The European Physical Journal Special Topics 231: 369–379.
• Ruiz-Silva, A., H. Gilardi-Velázquez, and E. Campos, 2021 Emergence of synchronous behavior in a network with chaotic multistable systems. Chaos, Solitons & Fractals 151: 111263.
• Tang, F., X. Zhao, and C. Li, 2023 Community detection in multilayer networks based on matrix factorization and spectral embedding method. Mathematics 11: 1573.
• Wang, X. F. and G. Chen, 2002 Synchronization in small-world dynamical networks. International Journal of Bifurcation and chaos 12: 187–192.
• Zhou, L. and C.Wang, 2016 Hybrid combinatorial synchronization on multiple sub-networks of complex network with unknown boundaries of uncertainties. Optik 127: 11037–11048.