Examples for

Dynamical Systems

Dynamical systems are a means of describing how one state evolves into subsequent states over the course of time. Oftentimes, dynamical systems exhibit chaotic and unpredictable behavior. Use Wolfram|Alpha's vast knowledge and computational power to explore concepts such as discrete- and continuous-time systems, control systems and fractals.

Discrete-Time Dynamical Systems

Examine the iterates, limiting behavior, etc. of discrete systems.

Analyze the logistic map:

Control Systems

Compute, analyze and plot properties of models representing the behavior of a variety of control systems.

Analyze a transfer function model:

Analyze a state-space model:

More examples

Continuous-Time Dynamical Systems

Find solutions, phase portraits, critical points, etc. of continuous dynamical systems.

Analyze the Van der Pol oscillator:

Analyze the Lotka–Volterra predator‐prey model:


  • Fractals