CHAOS AND COMPLEXITY | Colóquio DFMA
Transmissão via YouTube
Resumo: Many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner. This realisation has broad implications for many fields of science. Some basic concepts and properties in the field of chaotic dynamics of dissipative systems will be reviewed in this talk. I will use some of these properties in application topics, including the control of chaos in the heart and in the brain. I will then go a step further by arguing that a complex system are made up of many states that are interrelated in a complicated manner. The ability of a complex system to access those different states, combined with its sensitivity, offers great flexibility in manipulating the system’s dynamics to select a desired behaviour. Another important issue is the question of mathematical modelling of chaotic and complex systems, including complex networks. Mathematical modellers of such systems need to understand and take seriously the question of their own limitations.
Controlling complexity, L. Poon and C. Grebogi, Phys. Rev. Lett. 75, 4023 (1995).
Controlling Chaotic Dynamical Systems, C. Grebogi and Y. C. Lai, Systems Control Lett. 31, 307 (1997).
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems, W.-X. Wang, Y.-C. Lai, and C. Grebogi, Phys. Reports. 644, 1-76 (2016).
Relativistic Quantum Chaos, L. Huang, H.-Y. Xu, C. Grebogi, and Y.-C. Lai, Phys. Reports 753 1-128 (2018).
Sudden Regime Shifts After Apparent Stasis, C. Grebogi, Phys. of Life Reviews 32, 41-43 (2020).
Tipping Point and Noise-induced Transients in Ecological Networks, Y. Meng, Y.-C. Lai, and C. Grebogi, J. Royal Soc. Interface 17, 20200645 (2020).
Machine Learning Prediction of Critical Transition and System Collapse, L.-W.Long, H. Fan, C. Grebogi, and Y.-C. Lai, Phys. Rev. Research 3, 013090(1-14)
(2021).
