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The Rössler attractor Rössler attractor as a stereogram with =, =, =. The Rössler attractor (/ ˈ r ɒ s l ər /) is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler in the 1970s.
The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor. A fixed point of a function or transformation is a point that is mapped to itself by the function or ...
The strange attractor of the Duffing oscillator, through 4 periods ... Derivation of the frequency response. Using the method of harmonic balance, ...
The frequency distribution of the logistic map with r = 4 has high density near both sides of [0, 1] and is least dense at x = 0.5. When r = 4, apart from chaotic orbits, there are also periodic orbits with any period.
An attractor is a stable point which is also called a "sink". The repeller is considered as an unstable point, which is also known as a "source". A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space.
The set of states that lead to an attractor is called the basin of the attractor. States which occur only at the beginning of trajectories (no trajectories lead to them), are called garden-of-Eden states [8] and the dynamics of the network flow from these states towards attractors. The time it takes to reach an attractor is called transient ...
Period doubling in the Kuramoto–Sivashinsky equation with periodic boundary conditions. The curves depict solutions of the Kuramoto–Sivashinsky equation projected onto the energy phase plane (E, dE/dt), where E is the L 2-norm of the solution.
The Feigenbaum scaling function provides a complete description of the attractor of the logistic map at the end of the period-doubling cascade. The attractor is a Cantor set , and just as the middle-third Cantor set, it can be covered by a finite set of segments, all bigger than a minimal size d n .