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Introduction to the Modeling and Analysis of Complex Systems

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Introduction to the Modeling and Analysis of Complex Systems

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways.

Scientific Computing Simulations and ModelingMathematics
Author
Hiroki Sayama
Publisher
Binghamton University, State University of New York
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 110 sections
  1. 01: Introduction to Modeling and Analysis
  2. 1.01: Complex Systems in a Nutshell
  3. 1.02: Topical Clusters
  4. 02: Fundamentals of Modeling
  5. 2.01: Models in Science and Engineering
  6. 2.02: How to Create a Model
  7. 2.03: Modeling Complex Systems
  8. 2.04: What Are Good Models
  9. 2.05: A Historical Perspective
  10. 03: Basics of Dynamical Systems
  11. 3.01: What are Dynamical Systems?
  12. 3.02: Phase Space
  13. 3.03: What Can We Learn?
  14. 04: DiscreteTime Models I Modeling
  15. 401: DiscreteTime Models with Difference Equations
  16. 402: Classications of Model Equations
  17. 403: Simulating DiscreteTime Models with One Variable
  18. 404: Simulating DiscreteTime Models with Multiple Variables
  19. 405: Building Your Own Model Equation
  20. 406: Building Your Own Model Equations with Multiple Variables
  21. 05: DiscreteTime Models II Analysis
  22. 5.01: Finding Equilibrium Points
  23. 5.02: 5.2 Phase Space Visualization of Continuous-State Discrete-Time Models
  24. 5.03: 5.3 Cobweb Plots for One-Dimensional Iterative Maps
  25. 5.04: 5.4 Graph-Based Phase Space Visualization of Discrete-State Discrete-Time Model
  26. 5.05: Variable Rescaling of Discrete-Time Models
  27. 5.06: Asymptotic Behavior of Discrete-Time Linear Dynamical Systems
  28. 5.07: 5.7 Linear Stability Analysis of Discrete-Time Nonlinear Dynamical Systems
  29. 06: ContinuousTime Models I Modeling
  30. 6.01: Continuous-Time Models with Differential Equations
  31. 6.02: Classifications of Model Equation
  32. 6.03: Connecting Continuous - Time Models with DiscreteTime Models
  33. 6.04: Simulating Continuous-Time Models
  34. 6.05: Building Your Own Model Equation
  35. 07: ContinuousTime Models II Analysis
  36. 7.01: Finding Equilibrium Points
  37. 7.02: Phase Space Visualization
  38. 7.03: Variable Rescaling of Continuous-Time Models
  39. 7.04: Asymptotic Behavior of Continuous-Time Linear Dynamical Systems
  40. 7.05: Linear Stability Analysis of Nonlinear Dynamical Systems
  41. 08: Bifurcations
  42. 8.01: 8.1 What are Bifurcations?
  43. 8.02: Bifurcations in 1-D Continuous-Time Models
  44. 8.03: Hopf Bifurcations in 2-D Continuous-Time Models
  45. 8.04: Bifurcations in Discrete-Time Models
  46. 09: Chaos
  47. 9.01: Chaos in Discrete-Time Models
  48. 9.02: Characteristics of Chaos
  49. 9.03: Lyapunov Exponent
  50. 9.04: Chaos in Continuous-Time Model
  51. 10: Interactive Simulations of Complex Systems
  52. 10.01: Simulation of Systems with a Large Number of Variables
  53. 10.02: Interactive Simulation with PyCX
  54. 10.03: Interactive Parameter Control in PyCX
  55. 10.04: Simulation without PyCX
  56. 11: Cellular Automata I Modeling
  57. 11.01: Definition of Cellular Automata
  58. 11.02: Examples of Simple Binary Cellular Automata Rules
  59. 11.03: Simulating Cellular Automata
  60. 11.04: Extensions of Cellular Automata
  61. 11.05: Examples of Biological Cellular Automata Models
  62. 12: Cellular Automata II Analysis
  63. 12.01: Sizes of Rule Space and Phase Space
  64. 12.02: Phase Space Visualization
  65. 12.03: Mean-Field Approximation
  66. 12.04: Renormalization Group Analysis to Predict Percolation Thresholds
  67. 13: Continuous Field Models I Modeling
  68. 13.01: Continuous Field Models with Partial Differential Equations
  69. 13.02: Fundamentals of Vector Calculus
  70. 13.03: Visualizing Two-Dimensional Scalar and Vector Field
  71. 13.04: Modeling Spatial Movement
  72. 13.05: Simulation of Continuous Field Models
  73. 13.06: Reaction-Diffusion Systems
  74. 14: Continuous Field Models II Analysis
  75. 14.01: Finding Equilibrium States
  76. 14.02: Variable Rescaling
  77. 14.03: Linear Stability Analysis of Continuous Field Models
  78. 14.04: Linear Stability Analysis of Reaction-Diffusion Systems
  79. 15: Basics of Networks
  80. 15.01: Network Models
  81. 15.02: Terminologies of Graph Theory
  82. 15.03: Constructing Network Models with NetworkX
  83. 15.04: Visualizing Networks with NetworkX
  84. 15.05: Importing Exporting Network Data
  85. 15.06: Generating Random Graphs
  86. 16: Dynamical Networks I Modeling
  87. 16.01: Dynamical Network Models
  88. 16.02: Simulating Dynamics on Networks
  89. 16.03: Simulating Dynamics of Networks
  90. 16.04: Simulating Adaptive Networks
  91. 17: Dynamical Networks II Analysis of Network Topologies
  92. 17.01: Network Size, Density, and Percolation
  93. 17.02: Shortest Path Length
  94. 17.03: Centralities and Coreness
  95. 17.04: Clustering
  96. 17.05: Degree Distribution
  97. 17.06: Assortativity
  98. 17.07: Community Structure and Modularity
  99. 18: Dynamical Networks III Analysis of Network Dynamics
  100. 18.01: Dynamics of Continuous-State Networks
  101. 18.02: Diffusion on Networks
  102. 18.03: Synchronizability
  103. 18.04: Mean-Field Approximation of Discrete-State Networks
  104. 18.05: Mean-Field Approximation on Random Networks
  105. 18.06: Mean-Field Approximation on Scale-Free Networks
  106. 19: AgentBased Models
  107. 19.01: What Are Agent-Based Models?
  108. 19.02: Building an Agent-Based Model
  109. 19.03: Agent-Environment Interaction
  110. 19.04: Ecological and Evolutionary Models