The weather, the stock market, and the human heart are all examples of non-linear systems.
What is chaos theory?
Chaos theory studies the behavior of non-linear systems that are highly sensitive to initial conditions.
What is a attractor?
An attractor is a set of points that a dynamical system approaches over time.
What is the difference between a linear and a non-linear system?
A linear system has the property of superposition, which means that the output is proportional to the input, while a non-linear system does not.
What is a bifurcation?
A bifurcation is a sudden qualitative change in the behavior of a non-linear system that occurs as one or more parameters of the system are varied.
What is a fractal?
A fractal is a self-similar and non-integral geometric shape that can be generated by a simple iterative procedure.
What is the Lorenz attractor?
The Lorenz attractor is a set of chaotic solutions of a set of three ordinary differential equations that describe the behavior of the atmosphere.
What is the Mandelbrot set?
The Mandelbrot set is a set of complex numbers that, when iterated through a specific equation, do not escape to infinity.
What is a strange attractor?
A strange attractor is a type of chaotic attractor that has a fractal structure.
What is the butterfly effect?
The butterfly effect is the phenomenon where a small change in initial conditions can lead to large-scale and unpredictable effects in a non-linear system.
What is the Lyapunov exponent?
The Lyapunov exponent is a measure of the rate of divergence of nearby trajectories in a non-linear system.
What is a phase space?
A phase space is a mathematical space that describes all possible states of a system.
What is a Poincaré section?
A Poincaré section is a two-dimensional slice of a higher-dimensional phase space along a specific trajectory.
What is a bifurcation diagram?
A bifurcation diagram is a graphical representation of the behavior of a non-linear system as a parameter is varied.
What is the Feigenbaum constant?
The Feigenbaum constant is a mathematical constant that appears in the study of non-linear systems and period-doubling bifurcations.
What are some examples of non-linear systems?
The weather, the stock market, and the human heart are all examples of non-linear systems.
What is chaos theory?
Chaos theory studies the behavior of non-linear systems that are highly sensitive to initial conditions.
What is a attractor?
An attractor is a set of points that a dynamical system approaches over time.
What is the difference between a linear and a non-linear system?
A linear system has the property of superposition, which means that the output is proportional to the input, while a non-linear system does not.
What is a bifurcation?
A bifurcation is a sudden qualitative change in the behavior of a non-linear system that occurs as one or more parameters of the system are varied.
What is a fractal?
A fractal is a self-similar and non-integral geometric shape that can be generated by a simple iterative procedure.
What is the Lorenz attractor?
The Lorenz attractor is a set of chaotic solutions of a set of three ordinary differential equations that describe the behavior of the atmosphere.
What is the Mandelbrot set?
The Mandelbrot set is a set of complex numbers that, when iterated through a specific equation, do not escape to infinity.
What is a strange attractor?
A strange attractor is a type of chaotic attractor that has a fractal structure.
What is the butterfly effect?
The butterfly effect is the phenomenon where a small change in initial conditions can lead to large-scale and unpredictable effects in a non-linear system.
What is the Lyapunov exponent?
The Lyapunov exponent is a measure of the rate of divergence of nearby trajectories in a non-linear system.
What is a phase space?
A phase space is a mathematical space that describes all possible states of a system.
What is a Poincaré section?
A Poincaré section is a two-dimensional slice of a higher-dimensional phase space along a specific trajectory.
What is a bifurcation diagram?
A bifurcation diagram is a graphical representation of the behavior of a non-linear system as a parameter is varied.
What is the Feigenbaum constant?
The Feigenbaum constant is a mathematical constant that appears in the study of non-linear systems and period-doubling bifurcations.