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Joint Analysis and Applied Math Seminar
Dynamical approach to Self-Organized Criticality
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The concept of Self-Organized Criticality (SOC) was introduced by Bak, Tang and Wiesenfeld in 1987 as an attempt to give explanation of the omnipresence of fractal structures and power-law statistics in nature. SOC tends to explan a variety of phenomena, such as 1/f noise, earthquakes, forest fires, stock markets, biological evolution etc. Mathematical models were centralized around the original Per Bak's idea of idealized sandpile. Zhang continuous energy model is one of the most complicated of them and one believes it exhibits SOC in the thermodynamic limit (this was confirmed by physicists through numerical investigations). Impact of singularities makes an analytic investigation difficult. I will show certain rigorous results, such as calculation of entropy, estamates of Lyapunov spectrum and dimensional characteristics, and trace their asymptotics. This will explain loss of hyperbolicity in thermodynamic limit and confirm the power-law paradigm of SOC. The work is joint with my student Martin Rypdal. |