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0:00:00 Start 0:02:45 The Speakers... 0:15:47 Introduction 0:18:49 van Leeuwenhoek's estimate 0:19:28 Projections all use logistic curve 0:20:39 Carrying capacity K 0:21:54 Equilibrium versus steady-state 0:28:06 Stability classification of logistic Equ. 0:28:58 Relaxation time scale 0:29:45 Longer term view of population growth 0:30:58 Longer term view ... 0:32:31 von Foerester et al. (1960) 0:41:16 von Foerester et al. (1960) – the Doomsday date 0:46:00 Review of Johansen and Sornette(2001) – Physica A(vol. 294, 465-502) 0:47:49 Scaling and Complex Exponents 0:52:04 Example: Human population 0:52:41 Project idea 0:54:10 Complex Exponents 0:54:37 New way to fingerprint collapse in complex systems? 0:56:11 Vorticity Equation: Instantaneous version 0:58:19 Blow up in vorticity dynamics 1:00:03 Connection to critical points in complex systems 1:01:03 Critical points 1:02:03 Critical slowdown at equilibrium points 1:03:48 Critical slow-down 1:05:25 Discrete scal invariance 1:06:48 Project idea: A dynamical model exhibiting log-periodic oscillations 1:08:41 Salient points covered in the lecture: 1:09:17 Conclusion 1:09:44 Other ideas for group projects: