Understanding Complex Systems

Some Complex Systems Paradigms: Dynamical Systems Paradigm: When a System is Unstable or Chaotic, Discrete Master Equations privide more Accurate Models than the Correspnding Differential Equations (A. Gerig and A. Hubler, preprint) Harmony: Self-adjusting Systems Avoid Chaos => Adaptation to the Edge of Chaos P. Melby, J. Kaidel, N. Weber, A. Hubler, Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map, Phys.Rev.Lett 84 5991-5993 (2000) P. Melby, N. Weber, A. Hubler, Robustness of Adaptation in Controlled Self-adjusting Chaotic Systems, Phys. Fluctuation and Noise Lett. 2, L285-L292 (2002) Minimum Resistance: State of Least Resistance is Preferred M. Dueweke, U. Dierker, A. Hubler, Self-assembling Electrical Connections Based on the Principle of Minimum Resistance, Phys.Rev.E 54, 496-506 (1996) M. Sperl, A Chang, N. Weber, A. Hubler, Hebbian Learning in the Agglomeration of Conducting Particles, Phys.Rev.E. 59, 3165-3168 (1999) D. Smyth, A. Hubler, A Conductivity-Dependent Phase Transition from Closed-Loop to Open-Loop Dendritic Networks, Complexity 9, 56-60(2003). Joseph K. Jun and Alfred W. Hubler, Formation and structure of ramified charge transportation networks in an electromechanical system, PNAS 102, 536–540 (2005). Prediction of Chaos: Long Term Behavior Originates at Singular Points (V. Strelioff and A. Hubler, preprint) Control of Chaos: Equal Attention to All Relevant Variables => Success A. Hubler, Adaptive Control of Chaotic Systems, Helv.Phys,Acta 62,343 (1989) B. Plapp, A. Hubler, Nonlinear Resonances and Suppression of Chaos in the rf-Biased Josephson Junction, Phys.Rev.Lett 65, 2303-2306 (1990) Leadership: Agent with the Largest Moment of Surprise Wins Competition A. Hubler, D. Pines, Prediction and Adaptation in an Evolving Chaotic Environment, in Complexity: From Metapher to Reality, G. Cowan, D. Pines, G. Meltzer (Eds.), Adison-Wesley, 1994, 42 pages D. Pierre, A. Hubler, A Theory for Adaptation and Competition Applied to Logistic Map Dynamics, Physica D 75, 343-360 (1994) Nonlinear Resonances: Nonlinear Dynamical Systems React Most Sensitiv to their Own Dynamics G. Foster, A. Hubler, Robust and Efficient Interaction with Complex Systems, Proceedings of 2003 IEEE International Conference on Systems, Man & Cybernetics, 2029-2034(2003) J.Xu, A. Hubler, Enhanced Diffraction Pattern from a Fibonnaci Chain, Phys.Rev.B 67, 184202(2003) A. Hubler, U. Kuhl, R. Wittmann, T. Nagata, Sharp Diffraction Peaks from Chaotic Structures, CHAOS 7, 577-589 (1997) C. Wargitsch, A. Hubler, Resonances of Nonlinear Oscillators, Phys.Rev.E 51 1508-1519 (1995) Glenn Foster, Alfred W. Hübler, Karin Dahmen, Resonant forcing of multi-dimensional chaotic map dynamics, to appesr in Phys. Rev. E 2007 G. Foster, A. Hubler, K. Dahmen, Resonance Spectroscopy with Chaotic Forcing Functions, preprint 2007 Clock Paradigm: The fast clock locks the slow clock. Quatization of Emergent Structures: Dissipative Wave Particle Systems tend to have Attractors which are Separated in Space. The Whole is More than the Sum of the Parts: When the Top-Down and the Bottom-Up Sequences of Symmetry Breakings Match the Must Stable Structures Emerge. Alfred W. Hubler, Predicting Complex Systems with a Holistic Approach, Complexity 10, 11-16 (2005)