Modeling Complex Systems
This book explores the process of modeling complex systems in the widest sense of that term, drawing on examples from such diverse fields as ecology, epidemiology, sociology, seismology, as well as economics. It also provides the mathematical tools for studying the dynamics of these systems.nbsp;Boccara takes a carefully inductive approach in defining what it means for a system to be "complex" (and at the same time addresses the equally elusive concept of emergent properties).nbsp;This is the first text on the subject to draw comprehensive conclusions from such a wide range of analogous phenomena.
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asymptotically stable attractor automata average bifurcation diagram bifurcation point Boccara cells cellular automaton cellular automaton rule characteristic path length clustering coefficient configuration defined degree probability distribution denotes differential equation edges eigenvalues empty epidemic equal equilibrium point Example exhibits exists exponent exponential finite fixed point given hyperbolic equilibrium point infective individuals integer interactions interval iterations LÚvy limit cycle linear logistic map Lyapunov map f Mathematical matrix mean-field move neighborhood neighbors nonhyperbolic nonzero one-dimensional parameter pedestrian percolation period-doubling bifurcations phase space phase transition Physical Review population positive power-law behavior predator prey probability density function probability distribution random variable random walkers recurrence equation resp result rule f self-organized criticality sequence shows small-world small-world network solution species square lattice strategy susceptible theorem tion transcritical bifurcation two-dimensional unstable vector field vertex degree vertex degree probability vertices zero