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Dynamics

A system where the state at a certain point in time is represented by its past state is called a dynamical system. For example, if we have $x_{n}$ and it can be expressed as $x_{n+1} = f(x_{n})$ for some map $f$, or if the state of $x$ can be represented by a differential equation like $\dot{x} = g(x)$ for some function $g$, we can consider such cases. A system where deterministic values are obtained is called a dynamical system, while a non-deterministic system is called a stochastic process.1

Dynamics is a branch of mathematics that provides a mathematical approach to these dynamical systems, including mathematical modeling and system analysis. Despite its low recognition in Korea, it is a significant field widely applied in physics, chemistry, biology, business, and more. It is actively used not only in abstract exploration of space and time but also in practical problem-solving.

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Chaos
🟢Bio

General Dynamics

Sets and Spaces

Maps

Differential Equations

Bifurcation Theory

Mathematical Modeling

Population Growth

Disease Spread

Coupling

Nonsmooth Systems

Simulation

Cellular Automata

Agent-Based Simulation

Lattice Model Simulation

Key References

  • Allen. (2006). An Introduction to Mathematical Biology
  • Ottar N. Bjørnstad. (2018). Epidemics Models and Data using R
  • Capasso. (1993). Mathematical Structures of Epidemic Systems
  • Guckenheimer. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
  • Kuznetsov. (1998). Elements of Applied Bifurcation Theory(2nd Edition)
  • Strogatz. (2015). Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering(2nd Edition)
  • Yorke. (1996). CHAOS: An Introduction to Dynamical Systems
  • Wiggins. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos Second Edition(2nd Edition)

  1. Yorke. (1996). CHAOS: An Introduction to Dynamical Systems, p. 2. ↩︎


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