Introduction to the Modeling and Analysis of Complex Systems

INDEX 477partial differential equation, 8, 201, 227path, 299pattern formation, 8percolation, 206period-doubling bifurcation, 146periodic boundaries, 189periphery, 379perturbation, 90phase coherence, 345phase space, 31, 50phase transition, 199pitchfork bifurcation, 135planar graph, 300Poincaré-Bendixson theorem, 167positive assortativity, 397power law, 354predator-prey interaction, 55predator-prey model, 107preferential attachment, 354PyCX, 19, 174pylab, 42Python, 19, 39quiescent state, 189radius, 186, 379random graph, 320random regular graph, 321reaction term, 259reaction-diffusion system, 259, 286recurrence equation, 30regular graph, 300renormalization group analysis, 219robustness, 21rotation, 88rotational symmetry, 186roulette selection, 355rule-based modeling, 14saddle point, 94saddle-node bifurcation, 134scalar field, 228scale, 4scale-free network, 295, 355Schelling’s segregation model, 434selection, 459self-loop, 302self-organization, 6, 83self-organized criticality, 208separable PDE, 280separation of variables, 280short-range activation, 202shortest path length, 377sigmoid function, 443simple graph, 302simplicity, 4, 21simulation, 19, 39simultaneous updating, 48SIR model, 112, 128SIS model, 333, 416small-world network, 295, 349small-world problem, 349smoothness, 229social contagion, 365social network analysis, 295soft computing, 8spatial boundary condition, 189spatial derivative, 228spatial frequency, 279spectral gap, 407spectrum, 89spiral focus, 94, 126spontaneous pattern formation, 201, 247stability, 85, 122state transition, 74state variable, 30