Chaos in One Innocent Equation
What is chaos?
It is a seemingly random behavior exhibited in a system, with sensitive dependence on initial conditions. What we mean by ‘seemingly random’, is that this behavior is very unpredictable — so much so that it may appear random. This random appearance is due to the fact that the changes in behavior are extremely sensitive to the initial conditions of the dynamical system. In essence, chaos is the study of small changes that significantly change the future of a system.
What is a Dynamical System?
It is a system that can be described with a function with time dependence of a point in geometrical space. It is a system whose state evolves with time over a state space according to a dynamical law/rule. Simply put — it is the evolution of a system over time.
To understand the basic philosophy of what makes a dynamical system what it is, check out this article:
Examples of dynamical systems:
- a swinging pendulum
- the flow of water from a faucet
