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Download as PDF; Printable version ... CM Place, An introduction to dynamical systems, Cambridge University Press, 1990. ... Locking, and Chaos in a Dissipative ...
The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions.
Download as PDF; Printable version; In other projects ... (dynamical systems). List of chaotic maps. Map ... Li symmetrical toroidal chaos [38] continuous: real: 3:
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Deterministic system (mathematics) Linear system; Partial differential equation; Dynamical systems and chaos theory; Chaos theory. Chaos argument; Butterfly effect; 0-1 test for chaos; Bifurcation diagram; Feigenbaum constant; Sharkovskii's theorem; Attractor. Strange nonchaotic attractor; Stability theory. Mechanical equilibrium; Astable ...
A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system. A period-doubling cascade is an infinite sequence of period-doubling bifurcations. Such cascades are one route by which dynamical systems can develop chaos. [1] In hydrodynamics, they are one of the possible routes to ...
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by ...
In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model [1]) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, [2] and studied by Martin Gutzwiller in the 1980s, [3] [4] it is the first dynamical system to be proven chaotic.