Introduction to the Modeling and Analysis of Complex Systems

CONTENTSxviiIII Systems with a Large Number of Variables 17110 Interactive Simulation of Complex Systems 17310.1 Simulation of Systems with a Large Number of Variables . . . . . . . . . . . 17310.2 Interactive Simulation with PyCX . . . . . . . . . . . . . . . . . . . . . . . . 17410.3 Interactive Parameter Control in PyCX . . . . . . . . . . . . . . . . . . . . . 18010.4 Simulation without PyCX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18111 Cellular Automata I: Modeling 18511.1 Definition of Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . 18511.2 Examples of Simple Binary Cellular Automata Rules . . . . . . . . . . . . . 19011.3 Simulating Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . . 19211.4 Extensions of Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . 20011.5 Examples of Biological Cellular Automata Models . . . . . . . . . . . . . . . 20112 Cellular Automata II: Analysis 20912.1 Sizes of Rule Space and Phase Space . . . . . . . . . . . . . . . . . . . . . 20912.2 Phase Space Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . 21112.3 Mean-Field Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21512.4 Renormalization Group Analysis to Predict Percolation Thresholds . . . . . 21913 Continuous Field Models I: Modeling 22713.1 Continuous Field Models with Partial Differential Equations . . . . . . . . . 22713.2 Fundamentals of Vector Calculus . . . . . . . . . . . . . . . . . . . . . . . . 22913.3 Visualizing Two-Dimensional Scalar and Vector Fields . . . . . . . . . . . . 23613.4 Modeling Spatial Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . 24113.5 Simulation of Continuous Field Models . . . . . . . . . . . . . . . . . . . . . 24913.6 Reaction-Diffusion Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 25914 Continuous Field Models II: Analysis 26914.1 Finding Equilibrium States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26914.2 Variable Rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27314.3 Linear Stability Analysis of Continuous Field Models . . . . . . . . . . . . . 27514.4 Linear Stability Analysis of Reaction-Diffusion Systems . . . . . . . . . . . 28515 Basics of Networks 29515.1 Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29515.2 Terminologies of Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . 296