J. L. ECHENAUSÍA-MONROY, J.r. CUENSTA-GARCÍA, J. PENA RAMİREZ

The Wonder World of Complex Systems

Complex systems pervade nature and form the core of many technological applications. An exciting feature of these systems is that they exhibit a wide range of temporal behaviors, ranging from collective motion, synchronization, pattern formation, and chaos, among others. This has not only caught the attention of scientists, but also the interest of a wider audience. Consequently, our goal in this work is to provide a simple but descriptive explanation of some concepts related to complex systems. Specifically, the reader embarks on a journey that begins in the 17th century with the discovery of synchronization by Dutch scientist Christiaan Huygens and ends in the chaotic world explored by meteorologist Edward Lorenz around 1963. The journey is filled with examples, including synchronized clocks and metronomes, electronic fireflies that flash harmoniously, and even a chaotic dress.

Keywords:

Complex systems, Synchronization, Chaos Emergent behavior, Collective behavior, Chaotic dynamics,

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Abraham, N. B., A. M. Albano, A. Passamante, and P. E. Rapp, 2013 Measures of complexity and chaos, volume 208. Springer Science & Business Media.
Ambika, G., 2015 Ed lorenz: father of the ‘butterfly effect’. Resonance 20: 198–205.
Arellano-Delgado, A., C. Cruz-Hernández, R. López Gutiérrez, and C. Posadas-Castillo, 2015 Outer synchronization of simple firefly discrete models in coupled networks. Mathematical Problems in Engineering 2015.
Atmospheres, C., 2022 Strange attractors: Visualisation of chaotic equations. https://chaoticatmospheres.com/ mathrules-strange-attractors.
Barrio, R., S. Ibáñez, and L. Pérez, 2017 Hindmarsh–rose model: Close and far to the singular limit. Physics Letters A 381: 597– 603.
Buck, J. and E. Buck, 1976 Synchronous fireflies. Scientific American 234: 74–85.
Bulletin, U.-T.-I., 2019 Fashionable mathematics. https://issuu.com/ utokyo-iis/docs/utokyo-iis_bulletin_vol4/2?e=33831841/76398422. Chenciner, A., 2015 Poincaré and the three-body problem. In Henri Poincaré, 1912–2012, pp. 51–149, Springer.
Cuesta-García, J. R., 2022 El maravilloso mundo de los sistemas complejos: web site. https://complexity-net.org/.
Devaney, R. L., 2018 An introduction to chaotic dynamical systems. CRC press.
Drazin, P. G. and P. D. Drazin, 1992 Nonlinear systems. Number 10, Cambridge University Press.
Echenausía-Monroy, J. L., 2022a The beauty of chaos. https://youtu. be/Uou-FS_eHjM.
Echenausía-Monroy, J. L., 2022b Chaos and the double pendulum. https://youtu.be/SoNFulHypJQ.
Echenausía-Monroy, J. L., 2022c Hanging platform to synchronize metronomes. https://youtu.be/R-IcZJg1Qlo.
Echenausía-Monroy, J. L., 2022d Improving the shaker with chaos. https://youtu.be/hLdpnUWPdjM.
Echenausía-Monroy, J. L., 2022e Logistics dress: Chaos in fashion. https://youtu.be/GTsJ4Kg14TU.
Echenausía-Monroy, J. L., 2022f Lorenz and the butterfly effect. https://youtu.be/uYQvuNjVjBM.
Echenausía-Monroy, J. L., 2022g Monumental clocks synchronized. https://youtu.be/eQn3kzP8HU0.
Echenausía-Monroy, J. L., 2022h Synchronized electronic fireflies. https://youtu.be/yDTQx0rLvik.
Echenausía-Monroy, J. L., 2022i Synchronized metronomes on ice tea cans. https://youtu.be/Ng1bhcEaD-k.
Echenausía-Monroy, J. L., 2022j The wonder world of complex systems. https://youtu.be/eX3oShdvKFM.
Echenausía-Monroy, J. L., J. H. García-López, R. Jaimes-Reátegui, and G. Huerta-Cuéllar, 2020 Parametric control for multiscroll generation: Electronic implementation and equilibrium analysis. Nonlinear Analysis: Hybrid Systems 38: 100929.
Fujisaka, H. and T. Yamada, 1983 Stability theory of synchronized motion in coupled-oscillator systems. Progress of theoretical physics 69: 32–47.
Goldsztein, G. H., A. N. Nadeau, and S. H. Strogatz, 2021 Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales. Chaos: An Interdisciplinary Journal of Nonlinear Science 31: 023109.
Huerta-Cuéllar, G., E. Campos Cantón, and E. Tlelo-Cuautle, 2022 Complex Systems and Their Application (2022). (Eds.) Springer Cham, Switzerland.
Ladyman, J., J. Lambert, and K.Wiesner, 2013 What is a complex system? European Journal for Philosophy of Science 3: 33–67.
Larsen-Freeman, D. and L. Cameron, 2008 Complex systems and applied linguistics. Oxford University Press Oxford.
Lorenz, E., 2000 The butterfly effect. World Scientific Series on Nonlinear Science Series A 39: 91–94.
Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of Atmospheric Sciences 20: 130–141.
Martens, E. A., S. Thutupalli, A. Fourriere, and O. Hallatschek, 2013 Chimera states in mechanical oscillator networks. Proceedings of the National Academy of Sciences 110: 10563–10567.
May, R. M., 2004 Simple mathematical models with very complicated dynamics. In The Theory of Chaotic Attractors, pp. 85–93, Springer.
Núñez-Pérez, R. F., 2022 Prototipo de un nuevo mezclador electrónico pseudocaótico. Ingeniería, investigación y tecnología 23.
Osipov, G. V., J. Kurths, and C. Zhou, 2007 Synchronization in oscillatory networks. Springer Science & Business Media.
Ottino, J. M., 2003 Complex systems. American Institute of Chemical Engineers. AIChE Journal 49: 292.
Pena Ramirez, J. and H. Nijmeijer, 2020 The secret of the synchronized pendulums. Physics World 33: 36.
Pena Ramirez, J., L. A. Olvera, H. Nijmeijer, and J. Alvarez, 2016 The sympathy of two pendulum clocks: beyond huygens’ observations. Scientific reports 6: 1–16.
Pikovsky, A., J. Kurths, M. Rosenblum, and J. Kurths, 2003 Synchronization: a universal concept in nonlinear sciences. Number 12, Cambridge university press.
Ramirez, J. and H. Nijmeijer, 2016 The poincaré method: A powerful tool for analyzing synchronization of coupled oscillators. Indagationes Mathematicae 27: 1127–1146.
Shilnikov, A. and M. Kolomiets, 2008 Methods of the qualitative theory for the hindmarsh–rose model: A case study–a tutorial. International Journal of Bifurcation and Chaos 18: 2141–2168.
Sprott, J. C., 2010 Elegant chaos: algebraically simple chaotic flows. World Scientific.
Strogatz, S., 2004 Sync: The emerging science of spontaneous order. Penguin UK.
Wang, X. and J. Lu, 2019 Collective behaviors through social interactions in bird flocks. IEEE Circuits and Systems Magazine 19: 6–22.
Wolff, R. C., 1992 Local lyapunov exponents: looking closely at chaos. Journal of the Royal Statistical Society: Series B (Methodological) 54: 353–371.