"A model is a simplified representation of a system. It can be conceptual, verbal, diagrammatic, physical, or formal (mathematical)." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"A network (or graph) consists of a set of nodes (or vertices, actors) and a set of edges (or links, ties) that connect those nodes. [...] The size of a network is characterized by the numbers of nodes and edges in it." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"Chaos can be understood as a dynamical process in which microscopic information hidden in the details of a system’s state is dug out and expanded to a macroscopically visible scale (stretching), while the macroscopic information visible in the current system’s state is continuously discarded (folding)." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"Dynamics of a linear system are decomposable into multiple independent one-dimensional exponential dynamics, each of which takes place along the direction given by an eigenvector. A general trajectory from an arbitrary initial condition can be obtained by a simple linear superposition of those independent dynamics." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"Emergence is a nontrivial relationship between the properties of a system at microscopic and macroscopic scales. Macroscopic properties are called emergent when it is hard to explain them simply from microscopic properties." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"Self-organization is a dynamical process by which a system spontaneously forms nontrivial macroscopic structures and/or behaviors over time." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
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