Flashcards on Non-Linear Dynamics

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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.

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.

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