Introduction to the Modeling and Analysis of Complex Systems

INDEX 475equilibrium point, 61, 111equilibrium state, 269Erdős-Rényi random graph, 321Euler forward method, 105evolution, 8, 459evolutionary computation, 8excitable media, 202exclusive OR rule, 191exponential decay, 44exponential growth, 17, 44face validity, 21Fibonacci sequence, 38, 51Fick’s first law of diffusion, 242Fick’s second law of diffusion, 243field, 228first-order system, 37, 100fitness, 459FitzHugh-Nagumo model, 143fixed boundaries, 189flux, 241forest fire model, 206forest graph, 300fractal, 207fractal dimension, 164friendship paradox, 332, 421Fruchterman-Reingold force-directed algorithm,310Game of Life, 191game theory, 7Garden of Eden, 214gene regulatory network, 24genetic algorithm, 24geodesic distance, 377Gephi, 310giant component, 372, 374, 376global bifurcation, 131golden ratio, 84gradient, 229gradient field, 230graph, 76, 295, 296graph theory, 8, 295Gray-Scott model, 266heat equation, 243higher-order system, 37, 100homogeneous equilibrium state, 270homophily, 365Hopf bifurcation, 140Hopfield network, 346host-pathogen model, 204hub, 355hyperedge, 303hypergraph, 303hysteresis, 138in-degree centrality, 381inheritance, 459instability, 85, 122interactive simulation, 174invariant line, 86iterative map, 30, 38iterator, 327Jacobian matrix, 92, 126Karate Club graph, 309Keller-Segel model, 246, 440Kuramoto model, 342Laplacian, 234Laplacian matrix, 336, 407limit cycle, 140linear dynamical system, 81, 120linear operator, 276linear stability analysis, 90, 125, 275