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The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
Learn how a simple 3-dimensional differential equation discovered by Lorenz in 1963 can produce chaotic behavior and a strange attractor. Explore the fixed points, bifurcations, and homoclinic orbits of the Lorenz system.
Learn about the Lorenz equations, a simple model of convection and instability, and their chaotic dynamics on a strange attractor. See examples, diagrams and definitions of nonlinearity, symmetry, volume contraction, fixed points, linear stability, Hopf bifurcation, fractals and Lyapunov exponents.
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Learn about the Lorenz system, a set of differential equations that model convective motion in a fluid. Discover its history, symmetries, trapping region, global existence, equilibrium points, periodic orbits and Lyapunov exponents.
Sep 20, 2017 · Abstract. We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theory as a way to remove the singularities.
- Tali Pinsky
- 2017
This paper studies the Lorenz system of ordinary differential equations, which models convection in a fluid layer. It derives the fixed points, the potential function, the stability, and the phase portraits of the system, and shows how a parameter bifurcation leads to a chaotic attractor.
Oct 8, 2018 · The Lorenz equation played a role in confirming Hadamard’s counterexample concerning numerical experiments, finding examples for the catastrophe theory of Thom and Zeeman, and verifying the...
